What is the extreme e^x-2e^{-x}-3x ?

The extreme e^x-2e^{-x}-3x is Maximum(0,-1),Minimum(ln(2),-3ln(2)+1)

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extreme e^x-2e^{-x}-3x

extreme points

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

Maximum (0, - 1), Minimum (ln (2), - 3 ln (2) + 1)

Solution steps

f^{'} (x) = e^{x} + 2 e^{- x} - 3

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < ln (2),

Increasing

: ln (2) < x < \infty

Plug

x = 0

into

e^{x} - 2 e^{- x} - 3 x : - 1

Maximum (0, - 1)

Plug

x = ln (2)

into

e^{x} - 2 e^{- x} - 3 x : - 3 ln (2) + 1

Minimum (ln (2), - 3 ln (2) + 1)

Maximum (0, - 1), Minimum (ln (2), - 3 ln (2) + 1)

f (x) = x^{3} + 3 x^{2} - 4 x - 12

f (x) = x^{3} + 3 x^{2} - 24 x + 6

y = x^{3} - 6 x^{2} + 9 x + 1

f (x) = \frac{x ^{2}}{x ^{2} + 48}

f (x, y) = ln (3 - 4 x^{2} - 5 y^{2})

What is the extreme e^x-2e^{-x}-3x ?
The extreme e^x-2e^{-x}-3x is Maximum(0,-1),Minimum(ln(2),-3ln(2)+1)