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

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

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

extreme points

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

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 1

into

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

Maximum (- 1, 1)

Plug

x = 0

into

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

Minimum (0, 0)

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

f (x) = - 5 x^{2} + 50 x - 80

f (x) = 1 - 7 x^{2}

f (x) = - 12 x^{2} + 24 x

f (x) = 4 x + 4 sin (x)

t, x = 2 w

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