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

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

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

extreme points

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

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 1

into

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

Maximum (- 1, 1)

Plug

x = 0

into

2 x^{3} + 3 x^{2} : 0

Minimum (0, 0)

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

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