## Active forum topics

- 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
- Application of Differential Equation: Newton's Law of Cooling

## New forum topics

- 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
- Required diameter of solid shaft

## Recent comments

- Use integration by parts for…2 weeks ago
- need answer2 weeks ago
- Yes you are absolutely right…2 weeks 3 days ago
- I think what is ask is the…2 weeks 3 days ago
- $\cos \theta = \dfrac{2}{…2 weeks 4 days ago
- Why did you use (1/SQ root 5…2 weeks 4 days ago
- How did you get the 300 000pi2 weeks 4 days ago
- It is not necessary to…2 weeks 5 days ago
- Draw a horizontal time line…3 weeks 1 day ago
- Mali po ang equation mo…1 month 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=aand solve fory$9a^2 y = a(4a + a)^3$

$9a^2 y = 125a^4$

$y = \dfrac{125a^2}{9}$ ← not equal to 3

aKindly check the given.

## Ay sorry po.

In reply to I think something is wrong by Jhun Vert

## 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= 3a^{2}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

## 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

## Okay I got it. The given is

In reply to i-check ko. Anong page? by Jhun Vert

## May answer key po ba kayo

In reply to i-check ko. Anong page? by Jhun Vert

.

## $9a^3 y = x(4a - x)^3$

yin terms ofxusing 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 $9a^3 y'' = -4(4a - x)^2 - 8(4a - x)(a - x)$ $9a^3 y'' = -4(4a - x)[ (4a - x) + 2(a - x) ]$ $9a^3 y'' = -4(4a - x)(6a - 3x)$ $9a^3 y'' = -12(4a - x)(2a - x)$ Sety'to zero for maxima and/or minima $0 = 4(4a - x)^2 (a - x)$ For (4a-x)2 = 0:a, 0) is neither maximum nor minimuma-x= 0a, 0) is maximum.a= 1## Maraming Salamat po sir.

In reply to $9a^3 y = x(4a - x)^3$ by Jhun Vert

## Sir? Paano po naging (4a-4x)

## Okay na po pala sir hehe.

## May answer key po ba kayo

1

## y=x³-3x+1 Soln:

y=x³-3x+1

Soln: