What is the extreme f(x)=-1/3 x^3+2x^2-3x-12 ?

The extreme f(x)=-1/3 x^3+2x^2-3x-12 is Minimum(1,-40/3),Maximum(3,-12)

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extreme f(x)=-1/3 x^3+2x^2-3x-12

extreme points

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

Minimum (1, - \frac{40}{3}), Maximum (3, - 12)

Solution steps

f^{'} (x) = - x^{2} + 4 x - 3

Find intervals:

Decreasing

: - \infty < x < 1,

Increasing

: 1 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = 1

into

- \frac{1}{3} x^{3} + 2 x^{2} - 3 x - 12 : - \frac{40}{3}

Minimum (1, - \frac{40}{3})

Plug

x = 3

into

- \frac{1}{3} x^{3} + 2 x^{2} - 3 x - 12 : - 12

Maximum (3, - 12)

Minimum (1, - \frac{40}{3}), Maximum (3, - 12)

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

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

f (x, y) = 4 x^{3} + y^{3} - 12 x - 3 y

f (x, y) = 2 x^{4} + y^{2} - 16 x y

What is the extreme f(x)=-1/3 x^3+2x^2-3x-12 ?
The extreme f(x)=-1/3 x^3+2x^2-3x-12 is Minimum(1,-40/3),Maximum(3,-12)