Originally Posted by

**angypangy** I have a differentiation problem which starts with

$\displaystyle y = x^2 (4 - x)$

I have to find dy/dx. No problem there, get

$\displaystyle f'(x) = 8x - 3x^2$

Then to find values of x where dy/dy = 0

$\displaystyle x(8 - 3x) = 0$

$\displaystyle x = 0, x = \frac{8}{3}$

But then it asks "Denoting the values of x which you have just calculated by a and b, where a < b, show dy/dx is positive when a < x < b".

I can see graphically where dy/dx is positive, but do I need to show algebraically? How would I answer this?

Angus