What is the extreme f(x)=e^{x^3-12x+5} ?

The extreme f(x)=e^{x^3-12x+5} is Maximum(-2,e^{21}),Minimum(2, 1/(e^{11)})

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extreme f(x)=e^{x^3-12x+5}

extreme points

f (x) = e^{x^{3} - 12 x + 5}

Maximum (- 2, e^{21}), Minimum (2, \frac{1}{e ^{11}})

Solution steps

f^{'} (x) = e^{x^{3} - 12 x + 5} (3 x^{2} - 12)

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 2

into

e^{x^{3} - 12 x + 5} : e^{21}

Maximum (- 2, e^{21})

Plug

x = 2

into

e^{x^{3} - 12 x + 5} : \frac{1}{e ^{11}}

Minimum (2, \frac{1}{e ^{11}})

Maximum (- 2, e^{21}), Minimum (2, \frac{1}{e ^{11}})

f (x, y) = \frac{π}{3} \cdot y \cdot (x^{2} + 2.8 \cdot x + 7.84)

y = x re

ln (x^{2} + 8)

f (x, y) = x^{3} + 8 y^{3} - 6 x y + 5

f (x, y) = (- 3 x^{2} - 4 y^{2} - 9 x + 5 y + 3)

What is the extreme f(x)=e^{x^3-12x+5} ?
The extreme f(x)=e^{x^3-12x+5} is Maximum(-2,e^{21}),Minimum(2, 1/(e^{11)})