What is the extreme f(x)=-x^3-x^2+5x-3 ?

The extreme f(x)=-x^3-x^2+5x-3 is Minimum(-5/3 ,-256/27),Maximum(1,0)

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extreme f(x)=-x^3-x^2+5x-3

extreme

Minimum (- \frac{5}{3}, - \frac{256}{27}), Maximum (1, 0)

Solution steps

f^{'} (x) = - 3 x^{2} - 2 x + 5

Find intervals:

Decreasing

: - \infty < x < - \frac{5}{3},

Increasing

: - \frac{5}{3} < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - \frac{5}{3}

into

- x^{3} - x^{2} + 5 x - 3 : - \frac{256}{27}

Minimum (- \frac{5}{3}, - \frac{256}{27})

Plug

x = 1

into

- x^{3} - x^{2} + 5 x - 3 : 0

Maximum (1, 0)

Minimum (- \frac{5}{3}, - \frac{256}{27}), Maximum (1, 0)

What is the extreme f(x)=-x^3-x^2+5x-3 ?
The extreme f(x)=-x^3-x^2+5x-3 is Minimum(-5/3 ,-256/27),Maximum(1,0)