What is the extreme f(x)=e^x-7e^{-x}-8x ?

The extreme f(x)=e^x-7e^{-x}-8x is Maximum(0,-6),Minimum(ln(7),-8ln(7)+6)

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extreme f(x)=e^x-7e^{-x}-8x

extreme points

f (x) = e^{x} - 7 e^{- x} - 8 x

Maximum (0, - 6), Minimum (ln (7), - 8 ln (7) + 6)

Solution steps

f^{'} (x) = e^{x} + 7 e^{- x} - 8

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < ln (7),

Increasing

: ln (7) < x < \infty

Plug

x = 0

into

e^{x} - 7 e^{- x} - 8 x : - 6

Maximum (0, - 6)

Plug

x = ln (7)

into

e^{x} - 7 e^{- x} - 8 x : - 8 ln (7) + 6

Minimum (ln (7), - 8 ln (7) + 6)

Maximum (0, - 6), Minimum (ln (7), - 8 ln (7) + 6)

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

f (x) = x^{11} - 3 x^{9} + 2

f (x, y) = - 2.8 + x^{2} - 6.4 x y + 1.4 y^{2}

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

- x^{2} + 5

What is the extreme f(x)=e^x-7e^{-x}-8x ?
The extreme f(x)=e^x-7e^{-x}-8x is Maximum(0,-6),Minimum(ln(7),-8ln(7)+6)