Question

Determine all critical points for the function. f(x)=(x-10)^5

Answer 1

A critical point is just where a graph's slope is = to 0, so you can take the derivative of that function and set it equal to 0.

Using the chain rule:
f'(x) = 5(x-10)^4
0 = 5(x-10)^4

divide by 5 on both sides and take the 4th root of both sides.

0 = x - 10

add ten on both sides, and x = 10. Now, plug the x-value back into the original (you want to find the y-value on the original function ,not the derivative).

y = (10-10)^5 = 0

(10,0)