What is the extreme f(x)=6-3x^2-x^3 ?

The extreme f(x)=6-3x^2-x^3 is Minimum(-2,2),Maximum(0,6)

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extreme f(x)=6-3x^2-x^3

extreme points

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

Minimum (- 2, 2), Maximum (0, 6)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - 2

into

6 - 3 x^{2} - x^{3} : 2

Minimum (- 2, 2)

Plug

x = 0

into

6 - 3 x^{2} - x^{3} : 6

Maximum (0, 6)

Minimum (- 2, 2), Maximum (0, 6)

f (x) = x^{\frac{8}{3}}, - 1 \leq x \leq 8

12 x^{5} + 120 x^{4} - 300 x^{3}

f (x) = x + 2 cos (x), 0 \leq x \leq 2 π

f (x, y) = x^{2} y + 2 x y^{2} - 6 x y - 4

f (x) = 8 sin (2 x), - 2 π \leq x \leq 2 π

What is the extreme f(x)=6-3x^2-x^3 ?
The extreme f(x)=6-3x^2-x^3 is Minimum(-2,2),Maximum(0,6)