What is the extreme f(x)=-4x^3+2x^2-7 ?

The extreme f(x)=-4x^3+2x^2-7 is Minimum(0,-7),Maximum(1/3 ,-187/27)

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extreme f(x)=-4x^3+2x^2-7

extreme points

f (x) = - 4 x^{3} + 2 x^{2} - 7

Minimum (0, - 7), Maximum (\frac{1}{3}, - \frac{187}{27})

Solution steps

f^{'} (x) = - 12 x^{2} + 4 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{1}{3},

Decreasing

: \frac{1}{3} < x < \infty

Plug

x = 0

into

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

Minimum (0, - 7)

Plug

x = \frac{1}{3}

into

- 4 x^{3} + 2 x^{2} - 7 : - \frac{187}{27}

Maximum (\frac{1}{3}, - \frac{187}{27})

Minimum (0, - 7), Maximum (\frac{1}{3}, - \frac{187}{27})

- \frac{x ^{2}}{2} - 2 x

f (x) = 2 x^{3} + 3 x^{2} - 36 x

3 x^{2}

\frac{x}{x + 8} + \frac{x - 8}{x}

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

What is the extreme f(x)=-4x^3+2x^2-7 ?
The extreme f(x)=-4x^3+2x^2-7 is Minimum(0,-7),Maximum(1/3 ,-187/27)