For what values ofxdoes the graph off(x) have a horizontal tangent? (Round the answers to three decimal places.)f(x) = 4x3 + 9x2 + 4x+ 1

x1 = (smallerx-value)

x2 = (largerx-value)

how would i go about doing this problem

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- Nov 9th 2009, 07:19 PMkyleu03horizontal 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

*x*1 = (smaller*x*-value)

*x*2 = (larger*x*-value)

how would i go about doing this problem - Nov 9th 2009, 07:30 PMmr fantastic
- Nov 9th 2009, 07:34 PMBacterius
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__:

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