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

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

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

extreme

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

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

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

Minimum (0, 0)

Plug

x = 1

into

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

Maximum (1, 1)

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

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