What is the extreme f(x)=-x^3+3x^2+24x+5 ?

The extreme f(x)=-x^3+3x^2+24x+5 is Minimum(-2,-23),Maximum(4,85)

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extreme f(x)=-x^3+3x^2+24x+5

extreme points

f (x) = - x^{3} + 3 x^{2} + 24 x + 5

Minimum (- 2, - 23), Maximum (4, 85)

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 + 5 : - 23

Minimum (- 2, - 23)

Plug

x = 4

into

- x^{3} + 3 x^{2} + 24 x + 5 : 85

Maximum (4, 85)

Minimum (- 2, - 23), Maximum (4, 85)

y = (x + 2)^{2}

f (x) = 6 x - 6

y = \frac{1}{4} \cdot 2^{x - 20} + 2

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

\frac{2 x + 3}{4}

What is the extreme f(x)=-x^3+3x^2+24x+5 ?
The extreme f(x)=-x^3+3x^2+24x+5 is Minimum(-2,-23),Maximum(4,85)