find the intervals of increase and decrease of f(x) = e(adsbygoogle = window.adsbygoogle || []).push({}); ^{3x}+ e^{-2x}.

f'(x) = 3e^{3x}- 2e^{-2x}

I set f'(x) = 0 to find the critical numbers:

3e^{3x}= 2e^{-2x}

3 ln e^{3x}= 2 ln e^{-2x}

9x = -4x

x = 0, which is obviously wrong, (3e^0 - 2e^0 = 1). I found out that I had to combine the two terms using a common denomintor, and I got the right answer.

But why did my original method fail?

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# Homework Help: Intervals of increase/decrease with a exponential function

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