What is the extreme f(x)=-x^3+x^2+x-1 ?

The extreme f(x)=-x^3+x^2+x-1 is Minimum(-1/3 ,-32/27),Maximum(1,0)

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extreme f(x)=-x^3+x^2+x-1

extreme

Minimum (- \frac{1}{3}, - \frac{32}{27}), Maximum (1, 0)

Solution steps

f^{'} (x) = - 3 x^{2} + 2 x + 1

Find intervals:

Decreasing

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

Increasing

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

Decreasing

: 1 < x < \infty

Plug

x = - \frac{1}{3}

into

- x^{3} + x^{2} + x - 1 : - \frac{32}{27}

Minimum (- \frac{1}{3}, - \frac{32}{27})

Plug

x = 1

into

- x^{3} + x^{2} + x - 1 : 0

Maximum (1, 0)

Minimum (- \frac{1}{3}, - \frac{32}{27}), Maximum (1, 0)

What is the extreme f(x)=-x^3+x^2+x-1 ?
The extreme f(x)=-x^3+x^2+x-1 is Minimum(-1/3 ,-32/27),Maximum(1,0)