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,-26),Maximum(4,82)

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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, - 26), Maximum (4, 82)

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 : - 26

Minimum (- 2, - 26)

Plug

x = 4

into

- x^{3} + 3 x^{2} + 24 x + 2 : 82

Maximum (4, 82)

Minimum (- 2, - 26), Maximum (4, 82)

432 y^{783}

f (x) = 2 x^{3} - 3 x^{3} - 12 x + 1

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

f (x) = x^{4} + 4 x^{3} - 20 x^{2} + 1

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

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,-26),Maximum(4,82)