What is the extreme f(x)=12x^2+2x^3 ?

The extreme f(x)=12x^2+2x^3 is Maximum(-4,64),Minimum(0,0)

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extreme f(x)=12x^2+2x^3

extreme points

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

Maximum (- 4, 64), Minimum (0, 0)

Solution steps

f^{'} (x) = 24 x + 6 x^{2}

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 4

into

12 x^{2} + 2 x^{3} : 64

Maximum (- 4, 64)

Plug

x = 0

into

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

Minimum (0, 0)

Maximum (- 4, 64), Minimum (0, 0)

What is the extreme f(x)=12x^2+2x^3 ?
The extreme f(x)=12x^2+2x^3 is Maximum(-4,64),Minimum(0,0)