Question

How do you determine at which the graph of the function `y=x^4-8x^2+2` has a horizontal tangent line?

Answer 1

The graph has horizontal tangents at `x = 0, 2 and -2`.

Explanation:

First differentiate.

`y' = 4x^3 - 16x`

Horizontal tangents will have a slope of `0`. Since `y'` represents the slope of the tangent at any given point, set `y'` to `0` and solve for `x`.

`0 = 4x^3 - 16x`

`0 = 4x(x^2 - 4)`

`0 = 4x(x + 2)(x - 2)`

`x = 0, 2, -2`

Hopefully this helps!