What is the extreme f(x)=-x^3+3x^2+9x+1 ?

The extreme f(x)=-x^3+3x^2+9x+1 is Minimum(-1,-4),Maximum(3,28)

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extreme f(x)=-x^3+3x^2+9x+1

extreme points

f (x) = - x^{3} + 3 x^{2} + 9 x + 1

Minimum (- 1, - 4), Maximum (3, 28)

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 + 1 : - 4

Minimum (- 1, - 4)

Plug

x = 3

into

- x^{3} + 3 x^{2} + 9 x + 1 : 28

Maximum (3, 28)

Minimum (- 1, - 4), Maximum (3, 28)

\frac{5 x}{x ^{2} - 16}

4 x^{3} + 7 x^{2} - 20 x + 9

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

3 x^{7} - x^{5} - 7 x^{4} - 2 x^{3} + 3 x^{2}

2 x + 4 - 1

What is the extreme f(x)=-x^3+3x^2+9x+1 ?
The extreme f(x)=-x^3+3x^2+9x+1 is Minimum(-1,-4),Maximum(3,28)