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Popular >

extreme f(x)=e^{3x}+e^{-3x}

Solution

extreme points

f (x) = e^{3 x} + e^{- 3 x}

Solution

Minimum (0, 2)

Solution steps

f^{'} (x) = e^{3 x} \cdot 3 - 3 e^{- 3 x}

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \infty

Plug

x = 0

into

e^{3 x} + e^{- 3 x} : 2

Minimum (0, 2)

Popular Examples

symmetry x^3*3 symmetry

x^{3} \cdot 3

inverse of f(x)=-3sqrt(x-6)+5 inverse

f (x) = - 3 x - 6 + 5

asymptotes of f(x)=(-2x-8)/(x^2+6x+8)asymptotes

f (x) = \frac{- 2 x - 8}{x ^{2} + 6 x + 8}

range of 1/((x+2)(x-3))range

\frac{1}{( x + 2 ) ( x - 3 )}

domain of (sqrt(x+2))/(x-5)domain

\frac{x + 2}{x - 5}

Frequently Asked Questions (FAQ)

What is the extreme f(x)=e^{3x}+e^{-3x} ?
The extreme f(x)=e^{3x}+e^{-3x} is Minimum(0,2)