What is the extreme f(x)=x^3+3x^2+1 ?

The extreme f(x)=x^3+3x^2+1 is Maximum(-2,5),Minimum(0,1)

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extreme f(x)=x^3+3x^2+1

extreme

Maximum (- 2, 5), Minimum (0, 1)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 2

into

x^{3} + 3 x^{2} + 1 : 5

Maximum (- 2, 5)

Plug

x = 0

into

x^{3} + 3 x^{2} + 1 : 1

Minimum (0, 1)

Maximum (- 2, 5), Minimum (0, 1)

What is the extreme f(x)=x^3+3x^2+1 ?
The extreme f(x)=x^3+3x^2+1 is Maximum(-2,5),Minimum(0,1)