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Popular >

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

Solution

extreme points

f (x) = e^{x} + e^{- x}

Solution

Minimum (0, 2)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \infty

Plug

x = 0

into

e^{x} + e^{- x} : 2

Minimum (0, 2)

Popular Examples

extreme 5x+9x^{-1}extreme points

5 x + 9 x^{- 1}

extreme f(x)=3x^3-3x^2+12x-5,-1<= x<= 1 extreme points

f (x) = 3 x^{3} - 3 x^{2} + 12 x - 5, - 1 \leq x \leq 1

extreme f(x,y)=ln(-x^2-y^2+4)extreme points

f (x, y) = ln (- x^{2} - y^{2} + 4)

extreme f(x)=3+(\sqrt[3]{x^3-1})/(x-3)extreme points

extreme f(x)=-2x^3+21x^2-36x+3 extreme points

f (x) = - 2 x^{3} + 21 x^{2} - 36 x + 3

Frequently Asked Questions (FAQ)

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