Active forum topics
- Inverse Trigo
- General Solution of $y' = x \, \ln x$
- engineering economics: construct the cash flow diagram
- Eliminate the Arbitrary Constants
- Law of cosines
- Maxima and minima (trapezoidal gutter)
- Special products and factoring
- Integration of 4x^2/csc^3x√sinxcosx dx
- application of minima and maxima
- Sight Distance of Vertical Parabolic Curve
New forum topics
- Inverse Trigo
- General Solution of $y' = x \, \ln x$
- engineering economics: construct the cash flow diagram
- Integration of 4x^2/csc^3x√sinxcosx dx
- Maxima and minima (trapezoidal gutter)
- Special products and factoring
- Newton's Law of Cooling
- Law of cosines
- Can you help me po to solve this?
- Eliminate the Arbitrary Constants
Recent comments
- Yes.3 weeks 4 days ago
- Sir what if we want to find…3 weeks 4 days ago
- Hello po! Question lang po…1 month 1 week ago
- 400000=120[14π(D2−10000)]
(…2 months 2 weeks ago - Use integration by parts for…3 months 2 weeks ago
- need answer3 months 2 weeks ago
- Yes you are absolutely right…3 months 2 weeks ago
- I think what is ask is the…3 months 2 weeks ago
- $\cos \theta = \dfrac{2}{…3 months 2 weeks ago
- Why did you use (1/SQ root 5…3 months 2 weeks ago
I think something is wrong
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.
Ay sorry po.
In 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
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.
Kinuha ko kasi sa libro ni
In 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?
In reply to Kinuha ko kasi sa libro ni by Francis June E…
i-check ko. Anong page?
62-64 sir
In reply to i-check ko. Anong page? by Jhun Vert
62-64 sir
Okay I got it. The given is
In 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
In reply to i-check ko. Anong page? by Jhun Vert
.
$9a^3 y = x(4a - x)^3$
$9a^3 y = x(4a - x)^3$
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.
In 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)
Sir? Paano po naging (4a-4x) ? Yung sa simplify po
Okay na po pala sir hehe.
Okay na po pala sir hehe. Salamat po
May answer key po ba kayo
1
y=x³-3x+1 Soln:
y=x³-3x+1
Soln: