What is the extreme f(x)=-x^3+3x^2+24x-2 ?

The extreme f(x)=-x^3+3x^2+24x-2 is Minimum(-2,-30),Maximum(4,78)

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extreme f(x)=-x^3+3x^2+24x-2

extreme points

f (x) = - x^{3} + 3 x^{2} + 24 x - 2

Minimum (- 2, - 30), Maximum (4, 78)

Solution steps

f^{'} (x) = - 3 x^{2} + 6 x + 24

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = - 2

into

- x^{3} + 3 x^{2} + 24 x - 2 : - 30

Minimum (- 2, - 30)

Plug

x = 4

into

- x^{3} + 3 x^{2} + 24 x - 2 : 78

Maximum (4, 78)

Minimum (- 2, - 30), Maximum (4, 78)

\frac{1}{x ^{2} - 10 x + 25}

f (x) = x^{2} - 9

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

f (x) = 36 - 9 x^{2}

(- 3, - 6), (1, 4)

What is the extreme f(x)=-x^3+3x^2+24x-2 ?
The extreme f(x)=-x^3+3x^2+24x-2 is Minimum(-2,-30),Maximum(4,78)