What is the extreme f(x)=6+3x^2-2x^3 ?

The extreme f(x)=6+3x^2-2x^3 is Minimum(0,6),Maximum(1,7)

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extreme f(x)=6+3x^2-2x^3

extreme points

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

Minimum (0, 6), Maximum (1, 7)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = 0

into

6 + 3 x^{2} - 2 x^{3} : 6

Minimum (0, 6)

Plug

x = 1

into

6 + 3 x^{2} - 2 x^{3} : 7

Maximum (1, 7)

Minimum (0, 6), Maximum (1, 7)

What is the extreme f(x)=6+3x^2-2x^3 ?
The extreme f(x)=6+3x^2-2x^3 is Minimum(0,6),Maximum(1,7)