What is the extreme f(x)=10+12x-3x^2-2x^3 ?

The extreme f(x)=10+12x-3x^2-2x^3 is Minimum(-2,-10),Maximum(1,17)

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extreme f(x)=10+12x-3x^2-2x^3

extreme points

f (x) = 10 + 12 x - 3 x^{2} - 2 x^{3}

Minimum (- 2, - 10), Maximum (1, 17)

Solution steps

f^{'} (x) = - 6 x^{2} - 6 x + 12

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 2

into

10 + 12 x - 3 x^{2} - 2 x^{3} : - 10

Minimum (- 2, - 10)

Plug

x = 1

into

10 + 12 x - 3 x^{2} - 2 x^{3} : 17

Maximum (1, 17)

Minimum (- 2, - 10), Maximum (1, 17)

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

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

f (x) = x + y

f (x) = x^{\frac{2}{3}} (6 - x)^{\frac{1}{3}}

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

What is the extreme f(x)=10+12x-3x^2-2x^3 ?
The extreme f(x)=10+12x-3x^2-2x^3 is Minimum(-2,-10),Maximum(1,17)