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

The extreme f(x)=-x^3+3x^2+24x-3 is Minimum(-2,-31),Maximum(4,77)

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

extreme

Minimum (- 2, - 31), Maximum (4, 77)

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 - 3 : - 31

Minimum (- 2, - 31)

Plug

x = 4

into

- x^{3} + 3 x^{2} + 24 x - 3 : 77

Maximum (4, 77)

Minimum (- 2, - 31), Maximum (4, 77)

What is the extreme f(x)=-x^3+3x^2+24x-3 ?
The extreme f(x)=-x^3+3x^2+24x-3 is Minimum(-2,-31),Maximum(4,77)