What is the extreme f(x)=2+12x-x^3 ?

The extreme f(x)=2+12x-x^3 is Minimum(-2,-14),Maximum(2,18)

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extreme f(x)=2+12x-x^3

extreme points

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

Minimum (- 2, - 14), Maximum (2, 18)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 2

into

2 + 12 x - x^{3} : - 14

Minimum (- 2, - 14)

Plug

x = 2

into

2 + 12 x - x^{3} : 18

Maximum (2, 18)

Minimum (- 2, - 14), Maximum (2, 18)

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

f (x) = x^{3} - 12 x^{2} + 45 x + 1

3 ∣ x ∣

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

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

What is the extreme f(x)=2+12x-x^3 ?
The extreme f(x)=2+12x-x^3 is Minimum(-2,-14),Maximum(2,18)