What is the extreme f(x)=-x^3+3x^2+24x-1 ?

The extreme f(x)=-x^3+3x^2+24x-1 is Minimum(-2,-29),Maximum(4,79)

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extreme f(x)=-x^3+3x^2+24x-1

extreme points

f (x) = - x^{3} + 3 x^{2} + 24 x - 1

Minimum (- 2, - 29), Maximum (4, 79)

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 - 1 : - 29

Minimum (- 2, - 29)

Plug

x = 4

into

- x^{3} + 3 x^{2} + 24 x - 1 : 79

Maximum (4, 79)

Minimum (- 2, - 29), Maximum (4, 79)

g (x) = x 18 - x

5 x^{2} (x - 11) + 3

f (x) = x^{2} - y^{2} - 14 x + 4 y + 3

y x^{2} + 10 x = 10

f (x) = \frac{5 x}{x ^{2} + 2}

What is the extreme f(x)=-x^3+3x^2+24x-1 ?
The extreme f(x)=-x^3+3x^2+24x-1 is Minimum(-2,-29),Maximum(4,79)