Question

Find the maximum and the minimum values of `f(x)=3x^4-8x^3+6x^2` on `[-1/2,1/2]` by finding the points where the derivative is 0 and compering with the values at the end point?

Answer 1

`f'(x)=0`

`0=3x^4-8x^3+6x^2`

`0=(x^2)(3x^2-8x+6)`

use the quadratic formula to find that `3x^2-8x+6` have factors .610 and -3.277

`x= 0, .610, -3.277`

since range is [-.5, .5], x=0

find max/min value, plug x=0 into f(x)

compare answer with f(-.5) and f(.5)

you should be able to do the rest youself