Differentiating exponential functions

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October 1st 2010, 04:33 PM
blackdragon190

Differentiating exponential functions

I'm having trouble differentiating the function

$f(x)=axe^{(-bx)}$

where a and b are constants.

I'm supposed to show that the turning point occurs at

$x=1/b$

Using the product rule I get

$a(e^{-bx})+(ax)(-be^{-bx})$

But no matter what I do with that, I can't seem to get

$x=1/b$
October 1st 2010, 04:40 PM
skeeter

Quote:

Originally Posted by blackdragon190

I'm having trouble differentiating the function

$f(x)=axe^{(-bx)}$

where a and b are constants.

I'm supposed to show that the turning point occurs at

$x=1/b$

Using the product rule I get

$a(e^{-bx})+(ax)(-be^{-bx})$

But no matter what I do with that, I can't seem to get

$x=1/b$

$a \cdot e^{-bx}-abx \cdot e^{-bx} = 0$

$a \cdot e^{-bx}(1 - bx) = 0$

$x = \frac{1}{b}$
October 1st 2010, 04:46 PM
blackdragon190

Thank you :)

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