Question

How do you find the points where the graph of the function `F(x) = 4x^2 + 4x - 4` has horizontal tangents?

Answer 1

`(-1/2 , -5)`

Explanation:

The function will have horizontal tangents when f'(x) = 0

f(x) = `4x^2+4x-4 rArr f'(x) = 8x + 4`

now solve : 8x + 4 = 0 `rArr x = -1/2`

and `f(-1/2) = 4(-1/2)^2 + 4(-1/2) - 4 = -5`

hence `(-1/2 , -5)" is the point there is a horizontal tangent "`
graph{4x^2+4x-4 [-10, 10, -5, 5]}