What is the extreme f(x)=-x^3-x^2+5x+1 ?

The extreme f(x)=-x^3-x^2+5x+1 is Minimum(-5/3 ,-148/27),Maximum(1,4)

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extreme f(x)=-x^3-x^2+5x+1

extreme

Minimum (- \frac{5}{3}, - \frac{148}{27}), Maximum (1, 4)

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 + 1 : - \frac{148}{27}

Minimum (- \frac{5}{3}, - \frac{148}{27})

Plug

x = 1

into

- x^{3} - x^{2} + 5 x + 1 : 4

Maximum (1, 4)

Minimum (- \frac{5}{3}, - \frac{148}{27}), Maximum (1, 4)

What is the extreme f(x)=-x^3-x^2+5x+1 ?
The extreme f(x)=-x^3-x^2+5x+1 is Minimum(-5/3 ,-148/27),Maximum(1,4)