# For what x value does the tangent of the graph of f(x) = xe^2x have a slope = 0?

• April 4th 2010, 09:30 AM
satx
For what x value does the tangent of the graph of f(x) = xe^2x have a slope = 0?
I said

f'(x) = m = 0 = 2xe^2x ---> x = 0/(2xe^2x) = 0

Is this right?
• April 4th 2010, 09:37 AM
e^(i*pi)
Quote:

Originally Posted by satx
I said

f'(x) = m = 0 = 2xe^2x ---> x = 0/(2xe^2x) = 0

Is this right?

Your method is right although you need to use the product rule when finding $f'(x)$

$f(x) = xe^{2x}$

$u = x \: \rightarrow \: u' = 1$

$v = e^{2x} \: \rightarrow \: v' = 2e^{2x}$

$f'(x) = u'v + v'u$
• April 4th 2010, 09:41 AM
satx
Wouldn't that equal 2?
• April 4th 2010, 09:50 AM
Raoh
Quote:

Originally Posted by satx
Wouldn't that equal 2?

i believe you have, $f'(x)=2e^{2x}x+e^{2x}$
• April 4th 2010, 09:53 AM
Raoh
to solve $f'(x)=0$
$f'(x)=2e^{2x}x+e^{2x}=e^{2x}(2x+1)=0\Leftrightarro w 2x+1=0$
:)
• April 4th 2010, 09:54 AM
satx
Ok then that would equal one then, if x = 0, no? (e^2(0))(0) + e^2(0)) = 0 + 1 = 1???
• April 4th 2010, 09:55 AM
satx
Quote:

Originally Posted by Raoh
to solve $f'(x)=0$
$f'(x)=2e^{2x}x+e^{2x}=e^{2x}(2x+1)=0\Leftrightarro w 2x+1=0$
:)

So e^0 is 0? I'm so confused :(
• April 4th 2010, 09:56 AM
Raoh
Quote:

Originally Posted by satx
Ok then that would equal one then, if x = 0, no? (e^2(0))(0) + e^2(0)) = 0 + 1 = 1???

i think you're trying to solve $f'(x)=0$ :)
• April 4th 2010, 09:58 AM
satx
Quote:

Originally Posted by Raoh
i think you're trying to solve $f'(x)=0$ :)

Well isn't the slope equal to the derivative?
• April 4th 2010, 10:05 AM
Raoh
Quote:

Originally Posted by satx
So e^0 is 0? I'm so confused :(

well $e^0=1$,what i wrote means $f'(-\frac{1}{2})=0$ and the $x$ you're searching for is $-\frac{1}{2}$.
• April 4th 2010, 10:15 AM
Raoh
Quote:

Originally Posted by satx
Well isn't the slope equal to the derivative?

yes :)