What is the extreme f(x)=-x^3-4.5x^2+12x-2 ?

The extreme f(x)=-x^3-4.5x^2+12x-2 is Minimum(-4,-58),Maximum(1,4.5)

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extreme f(x)=-x^3-4.5x^2+12x-2

extreme points

f (x) = - x^{3} - 4.5 x^{2} + 12 x - 2

Minimum (- 4, - 58), Maximum (1, 4.5)

Solution steps

f^{'} (x) = - 3 x^{2} - 9 x + 12

Find intervals:

Decreasing

: - \infty < x < - 4,

Increasing

: - 4 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 4

into

- x^{3} - 4.5 x^{2} + 12 x - 2 : - 58

Minimum (- 4, - 58)

Plug

x = 1

into

- x^{3} - 4.5 x^{2} + 12 x - 2 : 4.5

Maximum (1, 4.5)

Minimum (- 4, - 58), Maximum (1, 4.5)

x^{2} y - x y + 3 y^{2}

\frac{6}{x ^{2} + 2}

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

\frac{6 x ^{2} - x ^{4}}{9}

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

What is the extreme f(x)=-x^3-4.5x^2+12x-2 ?
The extreme f(x)=-x^3-4.5x^2+12x-2 is Minimum(-4,-58),Maximum(1,4.5)