Minima Maxima: 9a³y=x(4a-x)³ Member for 6 years Submitted by Francis June E… on Thu, 04/09/2020 - 16:53 Patulong po ulit ako mam/sir Yung process po sana ulit 9a²y=x(4a+x)³ Yung ans nya po is (a,3a) maximum Thanks in advance mam/sir Tags Minima maxima Log in or register to post comments I think something is wrong Member for 17 years 6 months Jhun Vert Thu, 04/09/2020 - 17:13 I think something is wrong with your given. If you check for x = a, y ≠ 3a. Here is the checking of your answer key. Set x = a and solve for y $9a^2 y = a(4a + a)^3$ $9a^2 y = 125a^4$ $y = \dfrac{125a^2}{9}$ ← not equal to 3a Kindly check the given. Log in or register to post comments Ay sorry po. Member for 6 years Francis June E… Thu, 04/09/2020 - 18:15 In reply to I think something is wrong by Jhun VertAy sorry po. Eto po sir 9a²y=x(4a-x)³ Log in or register to post comments The same error. You can Member for 17 years 6 months Jhun Vert Thu, 04/09/2020 - 18:33 In reply to Ay sorry po. by Francis June E…The same error. You can evaluate if x = a, y = 3a2 not 3a. Either the given is wrong or the answer key is wrong. Log in or register to post comments Kinuha ko kasi sa libro ni Member for 6 years Francis June E… Thu, 04/09/2020 - 18:42 In reply to The same error. You can by Jhun VertKinuha ko kasi sa libro ni Love and Rainville yang example sir. Log in or register to post comments i-check ko. Anong page? Member for 17 years 6 months Jhun Vert Thu, 04/09/2020 - 19:00 In reply to Kinuha ko kasi sa libro ni by Francis June E…i-check ko. Anong page? Log in or register to post comments 62-64 sir Member for 6 years Francis June E… Fri, 04/10/2020 - 08:41 In reply to i-check ko. Anong page? by Jhun Vert62-64 sir Log in or register to post comments Okay I got it. The given is Member for 17 years 6 months Jhun Vert Fri, 04/10/2020 - 13:35 In reply to i-check ko. Anong page? by Jhun VertOkay I got it. The given is actually $9a^3 y = x(4a - x)^3$ Log in or register to post comments May answer key po ba kayo Member for 3 years 11 months Inah Mae Wed, 04/27/2022 - 10:54 In reply to i-check ko. Anong page? by Jhun Vert. Log in or register to post comments $9a^3 y = x(4a - x)^3$ Member for 17 years 6 months Jhun Vert Fri, 04/10/2020 - 22:02 $9a^3 y = x(4a - x)^3$ Differentiate y in terms of x using product formula $9a^3 y' = -3x(4a - x)^2 + (4a - x)^3$ Simplify (optional) $9a^3 y' = (4a - x)^2 [-3x + (4a - x)]$ $9a^3 y' = (4a - x)^2 (4a - 4x)$ $9a^3 y' = 4(4a - x)^2 (a - x)$ Determine the 2nd derivative $9a^3 y'' = -4(4a - x)^2 - 8(4a - x)(a - x)$ $9a^3 y'' = -4(4a - x)[ (4a - x) + 2(a - x) ]$ $9a^3 y'' = -4(4a - x)(6a - 3x)$ $9a^3 y'' = -12(4a - x)(2a - x)$ Set y' to zero for maxima and/or minima $0 = 4(4a - x)^2 (a - x)$ For (4a - x)2 = 0: $x = 4a$ $9a^3 y = 4a(4a - 4a)^3$ $y = 0$ Check if Maxima or Minima. $9a^3 y'' = -12(4a - 4a)(2a - 4a)$ $y'' = 0$ ← inflection point (the curve is neither upward nor downward) Hence, (4a, 0) is neither maximum nor minimum For a - x = 0 $x = a$ $9a^3 y = a(4a - a)^3$ $y = 3a$ Check if Maxima or Minima. $9a^3 y'' = -12(4a - a)(2a - a)$ $y'' = (-)$ ← the curve is concave downward Hence, (a, 0) is maximum. Here is the graph of the curve with a = 1 Log in or register to post comments Maraming Salamat po sir. Member for 6 years Francis June E… Fri, 04/10/2020 - 18:08 In reply to $9a^3 y = x(4a - x)^3$ by Jhun VertMaraming Salamat po sir. Godbless you po. :) Log in or register to post comments Sir? Paano po naging (4a-4x) Member for 6 years Francis June E… Fri, 04/10/2020 - 18:49 Sir? Paano po naging (4a-4x) ? Yung sa simplify po Log in or register to post comments Okay na po pala sir hehe. Member for 6 years Francis June E… Fri, 04/10/2020 - 19:27 Okay na po pala sir hehe. Salamat po Log in or register to post comments May answer key po ba kayo Member for 3 years 11 months Inah Mae Fri, 05/06/2022 - 03:10 1 Log in or register to post comments y=x³-3x+1 Soln: Member for 3 years 11 months Paul Adrian Wed, 04/27/2022 - 11:15 y=x³-3x+1 Soln: Log in or register to post comments
I think something is wrong Member for 17 years 6 months Jhun Vert Thu, 04/09/2020 - 17:13 I think something is wrong with your given. If you check for x = a, y ≠ 3a. Here is the checking of your answer key. Set x = a and solve for y $9a^2 y = a(4a + a)^3$ $9a^2 y = 125a^4$ $y = \dfrac{125a^2}{9}$ ← not equal to 3a Kindly check the given. Log in or register to post comments
Ay sorry po. Member for 6 years Francis June E… Thu, 04/09/2020 - 18:15 In reply to I think something is wrong by Jhun VertAy sorry po. Eto po sir 9a²y=x(4a-x)³ Log in or register to post comments
The same error. You can Member for 17 years 6 months Jhun Vert Thu, 04/09/2020 - 18:33 In reply to Ay sorry po. by Francis June E…The same error. You can evaluate if x = a, y = 3a2 not 3a. Either the given is wrong or the answer key is wrong. Log in or register to post comments
Kinuha ko kasi sa libro ni Member for 6 years Francis June E… Thu, 04/09/2020 - 18:42 In reply to The same error. You can by Jhun VertKinuha ko kasi sa libro ni Love and Rainville yang example sir. Log in or register to post comments
i-check ko. Anong page? Member for 17 years 6 months Jhun Vert Thu, 04/09/2020 - 19:00 In reply to Kinuha ko kasi sa libro ni by Francis June E…i-check ko. Anong page? Log in or register to post comments
62-64 sir Member for 6 years Francis June E… Fri, 04/10/2020 - 08:41 In reply to i-check ko. Anong page? by Jhun Vert62-64 sir Log in or register to post comments
Okay I got it. The given is Member for 17 years 6 months Jhun Vert Fri, 04/10/2020 - 13:35 In reply to i-check ko. Anong page? by Jhun VertOkay I got it. The given is actually $9a^3 y = x(4a - x)^3$ Log in or register to post comments
May answer key po ba kayo Member for 3 years 11 months Inah Mae Wed, 04/27/2022 - 10:54 In reply to i-check ko. Anong page? by Jhun Vert. Log in or register to post comments
$9a^3 y = x(4a - x)^3$ Member for 17 years 6 months Jhun Vert Fri, 04/10/2020 - 22:02 $9a^3 y = x(4a - x)^3$ Differentiate y in terms of x using product formula $9a^3 y' = -3x(4a - x)^2 + (4a - x)^3$ Simplify (optional) $9a^3 y' = (4a - x)^2 [-3x + (4a - x)]$ $9a^3 y' = (4a - x)^2 (4a - 4x)$ $9a^3 y' = 4(4a - x)^2 (a - x)$ Determine the 2nd derivative $9a^3 y'' = -4(4a - x)^2 - 8(4a - x)(a - x)$ $9a^3 y'' = -4(4a - x)[ (4a - x) + 2(a - x) ]$ $9a^3 y'' = -4(4a - x)(6a - 3x)$ $9a^3 y'' = -12(4a - x)(2a - x)$ Set y' to zero for maxima and/or minima $0 = 4(4a - x)^2 (a - x)$ For (4a - x)2 = 0: $x = 4a$ $9a^3 y = 4a(4a - 4a)^3$ $y = 0$ Check if Maxima or Minima. $9a^3 y'' = -12(4a - 4a)(2a - 4a)$ $y'' = 0$ ← inflection point (the curve is neither upward nor downward) Hence, (4a, 0) is neither maximum nor minimum For a - x = 0 $x = a$ $9a^3 y = a(4a - a)^3$ $y = 3a$ Check if Maxima or Minima. $9a^3 y'' = -12(4a - a)(2a - a)$ $y'' = (-)$ ← the curve is concave downward Hence, (a, 0) is maximum. Here is the graph of the curve with a = 1 Log in or register to post comments
Maraming Salamat po sir. Member for 6 years Francis June E… Fri, 04/10/2020 - 18:08 In reply to $9a^3 y = x(4a - x)^3$ by Jhun VertMaraming Salamat po sir. Godbless you po. :) Log in or register to post comments
Sir? Paano po naging (4a-4x) Member for 6 years Francis June E… Fri, 04/10/2020 - 18:49 Sir? Paano po naging (4a-4x) ? Yung sa simplify po Log in or register to post comments
Okay na po pala sir hehe. Member for 6 years Francis June E… Fri, 04/10/2020 - 19:27 Okay na po pala sir hehe. Salamat po Log in or register to post comments
May answer key po ba kayo Member for 3 years 11 months Inah Mae Fri, 05/06/2022 - 03:10 1 Log in or register to post comments
y=x³-3x+1 Soln: Member for 3 years 11 months Paul Adrian Wed, 04/27/2022 - 11:15 y=x³-3x+1 Soln: Log in or register to post comments
I think something is wrong
Member for
17 years 6 monthsI think something is wrong with your given. If you check for x = a, y ≠ 3a. Here is the checking of your answer key.
Set x = a and solve for y
$9a^2 y = a(4a + a)^3$
$9a^2 y = 125a^4$
$y = \dfrac{125a^2}{9}$ ← not equal to 3a
Kindly check the given.
Ay sorry po.
Member for
6 yearsIn reply to I think something is wrong by Jhun Vert
Ay sorry po.
Eto po sir 9a²y=x(4a-x)³
The same error. You can
Member for
17 years 6 monthsIn reply to Ay sorry po. by Francis June E…
The same error. You can evaluate if x = a, y = 3a2 not 3a. Either the given is wrong or the answer key is wrong.
Kinuha ko kasi sa libro ni
Member for
6 yearsIn reply to The same error. You can by Jhun Vert
Kinuha ko kasi sa libro ni Love and Rainville yang example sir.
i-check ko. Anong page?
Member for
17 years 6 monthsIn reply to Kinuha ko kasi sa libro ni by Francis June E…
i-check ko. Anong page?
62-64 sir
Member for
6 yearsIn reply to i-check ko. Anong page? by Jhun Vert
62-64 sir
Okay I got it. The given is
Member for
17 years 6 monthsIn reply to i-check ko. Anong page? by Jhun Vert
Okay I got it. The given is actually $9a^3 y = x(4a - x)^3$
May answer key po ba kayo
Member for
3 years 11 monthsIn reply to i-check ko. Anong page? by Jhun Vert
.
$9a^3 y = x(4a - x)^3$
Member for
17 years 6 months$9a^3 y = x(4a - x)^3$
Differentiate y in terms of x using product formula
$9a^3 y' = -3x(4a - x)^2 + (4a - x)^3$
Simplify (optional)
$9a^3 y' = (4a - x)^2 [-3x + (4a - x)]$
$9a^3 y' = (4a - x)^2 (4a - 4x)$
$9a^3 y' = 4(4a - x)^2 (a - x)$
Determine the 2nd derivative
$9a^3 y'' = -4(4a - x)^2 - 8(4a - x)(a - x)$
$9a^3 y'' = -4(4a - x)[ (4a - x) + 2(a - x) ]$
$9a^3 y'' = -4(4a - x)(6a - 3x)$
$9a^3 y'' = -12(4a - x)(2a - x)$
Set y' to zero for maxima and/or minima
$0 = 4(4a - x)^2 (a - x)$
For (4a - x)2 = 0:
$9a^3 y = 4a(4a - 4a)^3$
$y = 0$
Check if Maxima or Minima.
$9a^3 y'' = -12(4a - 4a)(2a - 4a)$
$y'' = 0$ ← inflection point (the curve is neither upward nor downward)
Hence, (4a, 0) is neither maximum nor minimum
For a - x = 0
$9a^3 y = a(4a - a)^3$
$y = 3a$
Check if Maxima or Minima.
$9a^3 y'' = -12(4a - a)(2a - a)$
$y'' = (-)$ ← the curve is concave downward
Hence, (a, 0) is maximum.
Here is the graph of the curve with a = 1
Maraming Salamat po sir.
Member for
6 yearsIn reply to $9a^3 y = x(4a - x)^3$ by Jhun Vert
Maraming Salamat po sir. Godbless you po. :)
Sir? Paano po naging (4a-4x)
Member for
6 yearsSir? Paano po naging (4a-4x) ? Yung sa simplify po
Okay na po pala sir hehe.
Member for
6 yearsOkay na po pala sir hehe. Salamat po
May answer key po ba kayo
Member for
3 years 11 months1
y=x³-3x+1 Soln:
Member for
3 years 11 monthsy=x³-3x+1
Soln: