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

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

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

extreme

Minimum (0, 2), Maximum (2, 6)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 0

into

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

Minimum (0, 2)

Plug

x = 2

into

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

Maximum (2, 6)

Minimum (0, 2), Maximum (2, 6)

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