What is the extreme f(x)= 1/4 e^x+e^{-x} ?

The extreme f(x)= 1/4 e^x+e^{-x} is Minimum(ln(2),1)

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extreme f(x)= 1/4 e^x+e^{-x}

extreme

Minimum (ln (2), 1)

Solution steps

f^{'} (x) = \frac{1}{4} e^{x} - e^{- x}

Find intervals:

Decreasing

: - \infty < x < ln (2),

Increasing

: ln (2) < x < \infty

Plug

x = ln (2)

into

\frac{1}{4} e^{x} + e^{- x} : 1

Minimum (ln (2), 1)

What is the extreme f(x)= 1/4 e^x+e^{-x} ?
The extreme f(x)= 1/4 e^x+e^{-x} is Minimum(ln(2),1)