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 ,-202/27),Maximum(1,2)

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

extreme points

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

Minimum (- \frac{5}{3}, - \frac{202}{27}), Maximum (1, 2)

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{202}{27}

Minimum (- \frac{5}{3}, - \frac{202}{27})

Plug

x = 1

into

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

Maximum (1, 2)

Minimum (- \frac{5}{3}, - \frac{202}{27}), Maximum (1, 2)

f (x) = e^{(x^{3} - 6 x^{2} + 8)}

y = 2 x - 1, (1, 1)

y = \frac{1}{4} x

f (x) = x x^{2} - 1

ln (2 x - 1)

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 ,-202/27),Maximum(1,2)