# Thread: horizontal tangent

1. ## horizontal tangent

For what values of x does the graph of f (x) have a horizontal tangent? (Round the answers to three decimal places.) f (x) = 4 x 3 + 9 x 2 + 4 x + 1
x1 = (smaller x-value)
x2 = (larger x-value)

how would i go about doing this problem

2. Originally Posted by kyleu03
For what values of x does the graph of f (x) have a horizontal tangent? (Round the answers to three decimal places.) f (x) = 4 x 3 + 9 x 2 + 4 x + 1
x1 = (smaller x-value)
x2 = (larger x-value)

how would i go about doing this problem
Solve f'(x) = 0.

3. A horizontal tangent means that the slope of the tangent is $\displaystyle 0$, right ? So you would basically get the derivative of your function and go hunting for solutions of $\displaystyle f'(x) = 0$.

Your function is : $\displaystyle f(x) = 4x^3 + 9x^2 + 4x + 1$ (I assume, since it isn't clear in your message)

Therefore, your derivative would be (don't click if you want to find by yourself) :

Spoiler:
$\displaystyle f'(x) = 12x^2 + 18x + 4$

Therefore, you would be solving $\displaystyle f'(x) = 0$, which is easy since $\displaystyle f'(x)$ is a quadratic equation. All right ?