What is the extreme f(x)=-x^3+3x^2+9x-6 ?

The extreme f(x)=-x^3+3x^2+9x-6 is Minimum(-1,-11),Maximum(3,21)

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extreme f(x)=-x^3+3x^2+9x-6

extreme points

f (x) = - x^{3} + 3 x^{2} + 9 x - 6

Minimum (- 1, - 11), Maximum (3, 21)

Solution steps

f^{'} (x) = - 3 x^{2} + 6 x + 9

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 1

into

- x^{3} + 3 x^{2} + 9 x - 6 : - 11

Minimum (- 1, - 11)

Plug

x = 3

into

- x^{3} + 3 x^{2} + 9 x - 6 : 21

Maximum (3, 21)

Minimum (- 1, - 11), Maximum (3, 21)

f (x, y) = \frac{x ^{2}}{8} + \frac{y ^{2}}{2} - 1

f (x) = x_{2} - x_{1}

3 x^{2} + 15 x + 18

- 2 x^{3} - 27 x^{2} - 84 x - 3

f (t) = (3 - t) u_{4} (t)

What is the extreme f(x)=-x^3+3x^2+9x-6 ?
The extreme f(x)=-x^3+3x^2+9x-6 is Minimum(-1,-11),Maximum(3,21)