What is the extreme f(x)= 1/2 (e^x+e^{-x}) ?

The extreme f(x)= 1/2 (e^x+e^{-x}) is Minimum(0,1)

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extreme f(x)= 1/2 (e^x+e^{-x})

extreme points

f (x) = \frac{1}{2} (e^{x} + e^{- x})

Minimum (0, 1)

Solution steps

f^{'} (x) = \frac{1}{2} (e^{x} - e^{- x})

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \infty

Plug

x = 0

into

\frac{1}{2} (e^{x} + e^{- x}) : 1

Minimum (0, 1)

f (x) = 2 x^{2} - 4 x^{4}

x^{3} + 6 x^{2} - 63 x + 10

f (x, y) = x^{2} + y^{2} + 10 x - 10 y + 5

f (x) = 2 x y - x^{3} - y^{2}

f (x) = x - sin (2 x), (- 1, 3)

What is the extreme f(x)= 1/2 (e^x+e^{-x}) ?
The extreme f(x)= 1/2 (e^x+e^{-x}) is Minimum(0,1)