What is the extreme f(x)=8+12x^2-8x^3 ?

The extreme f(x)=8+12x^2-8x^3 is Minimum(0,8),Maximum(1,12)

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extreme f(x)=8+12x^2-8x^3

extreme

Minimum (0, 8), Maximum (1, 12)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = 0

into

8 + 12 x^{2} - 8 x^{3} : 8

Minimum (0, 8)

Plug

x = 1

into

8 + 12 x^{2} - 8 x^{3} : 12

Maximum (1, 12)

Minimum (0, 8), Maximum (1, 12)

What is the extreme f(x)=8+12x^2-8x^3 ?
The extreme f(x)=8+12x^2-8x^3 is Minimum(0,8),Maximum(1,12)