`f(x) = e^(2x) + e^(-x)` (a) Find the intervals on which `f` is increasing or decreasing. (b) Find the local maximum and minimum values of `f`. (c) Find the intervals of concavity and the inflection points.
You need to determine where the function increases or decreases, hence, you need to verify where f'(x)>0 or f'(x)<0.
You need to determine derivative of the function:
`f'(x) = 2e^(2x) - e^(-x)`
Putting f'(x) = 0, yields:
`2e^(2x) - e^(-x) = 0`
`2e^(2x) - 1/(e^x) = 0 => 2e^(3x) - 1 = 0 => e^(3x) = 1/2 => e^x = root(3)(1/2)`
`x = ln...
(The entire section contains 196 words.)
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