## anonymous 4 years ago Determine all the critical points for the function f(x)= x^2 + (16/x)

1. freckles

You found f' yet?

2. anonymous

f '= 2x-(16/x^2)???

3. freckles

Yep! :)

4. freckles

Now combine fractions! :)

5. freckles

$f'=\frac{2x(x^2)-16}{x^2}$ right? :)

6. anonymous

Thats what I got! :)

7. freckles

Now set Mr.top=0! :) and solve for x We would look at where the bottom is 0 except our function is not even define for x=0 So we are only look for when the top of f' is 0

8. freckles

$2x(x^2)-16=0$

9. freckles

Can you solve this for x?

10. anonymous

x=2 ??

11. freckles

$2x^3-16=0$ Yes that is the only real critical number $x^3-8=0$ $(x-2)(x^2+2x+4)=0$ x=2 --- $b^2-4ac=2^2-4(1)(4)=4-16=-12 <0 => x=2 \text{ is the only critical number}$ :) So good job! :)

12. anonymous

Oh great! thank you

13. freckles

You deserve a medal! Seriously great job! :)