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,-27),Maximum(4,81)

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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, - 27), Maximum (4, 81)

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 : - 27

Minimum (- 2, - 27)

Plug

x = 4

into

- x^{3} + 3 x^{2} + 24 x + 1 : 81

Maximum (4, 81)

Minimum (- 2, - 27), Maximum (4, 81)

y = - 3 cos (2 x) - 2.5

f (x) = 3 (4)^{x}

e^{4 x}

x^{2} - 6 x + 4

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,-27),Maximum(4,81)