# horizontal tangent

• Nov 9th 2009, 07:19 PM
kyleu03
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
• Nov 9th 2009, 07:30 PM
mr fantastic
Quote:

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.
• Nov 9th 2009, 07:34 PM
Bacterius
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 ?