- #1
endeavor
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find the intervals of increase and decrease of f(x) = e3x + e-2x.
f'(x) = 3e3x - 2e-2x
I set f'(x) = 0 to find the critical numbers:
3e3x = 2e-2x
3 ln e3x = 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?
f'(x) = 3e3x - 2e-2x
I set f'(x) = 0 to find the critical numbers:
3e3x = 2e-2x
3 ln e3x = 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?