Question

Find the critical points and absolute extrema of:
f(x) = x^3-2x^2-5x+6 on [4,8]

Answer 1

I've gotten the derivative of:
\[f{'} = 3x^2-4x-5\]

Answer 2

I don't think it can be factored and i couldn't find any values that can bring this to zero, so would there be no critical points?

Answer 3

if anything, use the quadratic formula

Answer 4

its got 1 positive root gauarenteed byt he rule of sign ...

Answer 5

its a positive x^2 parabola that goes to positive infinity as x gets large, but at x=0 its value is -5

by default, it has to cross the x axis to get from -5 to +oo

Answer 6

the good news is that the intercepts are not withing the domain [4,8] so all thats left is to check the end points