What is the extreme f(x)=4+15x+6x^2-x^3 ?

The extreme f(x)=4+15x+6x^2-x^3 is Minimum(-1,-4),Maximum(5,104)

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extreme f(x)=4+15x+6x^2-x^3

extreme

Minimum (- 1, - 4), Maximum (5, 104)

Solution steps

f^{'} (x) = - 3 x^{2} + 12 x + 15

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 5,

Decreasing

: 5 < x < \infty

Plug

x = - 1

into

4 + 15 x + 6 x^{2} - x^{3} : - 4

Minimum (- 1, - 4)

Plug

x = 5

into

4 + 15 x + 6 x^{2} - x^{3} : 104

Maximum (5, 104)

Minimum (- 1, - 4), Maximum (5, 104)

What is the extreme f(x)=4+15x+6x^2-x^3 ?
The extreme f(x)=4+15x+6x^2-x^3 is Minimum(-1,-4),Maximum(5,104)