Question

How do you find the points where the graph of the function `f(x)= (x^2 + 3x - 10)^3` has horizontal tangents?

Answer 1

Find the points where `f'(x) = 0`

Explanation:

`f'(x) = 3(x^2+3x-10)(2x+3) = 0`

if and only if

`x^2+3x-10=0` `" "` or `" "` `2x+3=0`

`(x+5)(x-2)=0` `" "` or `" "` `2x+3=0`

`x = -1`, `2`, or `-3/2`