What is the extreme f(x)=-x^3+3x^2+24x-4 ?

The extreme f(x)=-x^3+3x^2+24x-4 is Minimum(-2,-32),Maximum(4,76)

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extreme f(x)=-x^3+3x^2+24x-4

extreme points

f (x) = - x^{3} + 3 x^{2} + 24 x - 4

Minimum (- 2, - 32), Maximum (4, 76)

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 - 4 : - 32

Minimum (- 2, - 32)

Plug

x = 4

into

- x^{3} + 3 x^{2} + 24 x - 4 : 76

Maximum (4, 76)

Minimum (- 2, - 32), Maximum (4, 76)

x^{2} + 4 x + 4

f (x) = \frac{x ^{2}}{ln ( x )}

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

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

f (x) = 6 x - 7 x^{\frac{6}{7}}

What is the extreme f(x)=-x^3+3x^2+24x-4 ?
The extreme f(x)=-x^3+3x^2+24x-4 is Minimum(-2,-32),Maximum(4,76)