What is the extreme f(x)=x^3+3x^2-45x ?

The extreme f(x)=x^3+3x^2-45x is Maximum(-5,175),Minimum(3,-81)

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extreme f(x)=x^3+3x^2-45x

extreme

Maximum (- 5, 175), Minimum (3, - 81)

Solution steps

f^{'} (x) = 3 x^{2} + 6 x - 45

Find intervals:

Increasing

: - \infty < x < - 5,

Decreasing

: - 5 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 5

into

x^{3} + 3 x^{2} - 45 x : 175

Maximum (- 5, 175)

Plug

x = 3

into

x^{3} + 3 x^{2} - 45 x : - 81

Minimum (3, - 81)

Maximum (- 5, 175), Minimum (3, - 81)

What is the extreme f(x)=x^3+3x^2-45x ?
The extreme f(x)=x^3+3x^2-45x is Maximum(-5,175),Minimum(3,-81)