Question

Determine all the critical points for the function f(x)= x^2 + (16/x)

Answer 1

You found f' yet?

Answer 2

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

Answer 3

Yep! :)

Answer 4

Now combine fractions! :)

Answer 5

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

Answer 6

Thats what I got! :)

Answer 7

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

Answer 8

\[2x(x^2)-16=0\]

Answer 9

Can you solve this for x?

Answer 10

x=2 ??

Answer 11

\[2x^3-16=0\]
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! :)

Answer 12

Oh great! thank you

Answer 13

You deserve a medal! Seriously great job! :)