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

The extreme f(x)=-12x^3+2x^2-3 is Minimum(0,-3),Maximum(1/9 ,-727/243)

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

extreme

Minimum (0, - 3), Maximum (\frac{1}{9}, - \frac{727}{243})

Solution steps

f^{'} (x) = - 36 x^{2} + 4 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{1}{9},

Decreasing

: \frac{1}{9} < x < \infty

Plug

x = 0

into

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

Minimum (0, - 3)

Plug

x = \frac{1}{9}

into

- 12 x^{3} + 2 x^{2} - 3 : - \frac{727}{243}

Maximum (\frac{1}{9}, - \frac{727}{243})

Minimum (0, - 3), Maximum (\frac{1}{9}, - \frac{727}{243})

What is the extreme f(x)=-12x^3+2x^2-3 ?
The extreme f(x)=-12x^3+2x^2-3 is Minimum(0,-3),Maximum(1/9 ,-727/243)