Finding Absolute Max and Min

[Fcpuyol]

Problem: Let f(x) = x^2/(2) + 8/(x). Find the absolute minimum and absolute maximum on [1,4]

I know I have to find f'(x) and set equal to 0 and find the the critical points. and plug in back to the original function x = 1, x = 0 and the critical points.

Work: f'(x) = x - 8(x)^(-2)
= x - 8/(x)^2 = 0

I just need some help on what to do when I set the f'(x) = 0. How exactly would I solve for x? Thanks

 

[Deleted member 4993]

Problem: Let f(x) = x^2/(2) + 8/(x). Find the absolute minimum and absolute maximum on [1,4]

I know I have to find f'(x) and set equal to 0 and find the the critical points. and plug in back to the original function x = 1, x = 0 and the critical points.

Work: f'(x) = x - 8(x)^(-2)
= x - 8/(x)^2 = 0

I just need some help on what to do when I set the f'(x) = 0. How exactly would I solve for x? Thanks

$\displaystyle \displaystyle{x \ - \ \frac{8}{x^2} \ = \ 0}$

$\displaystyle \displaystyle{x \ = \ \frac{8}{x^2}}$

$\displaystyle \displaystyle{x^3 - 2^3 \ = \ 0}$

$\displaystyle \displaystyle{(x - 2)(x^2 \ + \ 2x \ + \ 4)\ = \ 0}$

Continue....

Do not forget to check the end-points - since you are looking for absolute min/max.