What is the extreme f(x)=-x^3-x^2+5x-4 ?

The extreme f(x)=-x^3-x^2+5x-4 is Minimum(-5/3 ,-283/27),Maximum(1,-1)

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extreme f(x)=-x^3-x^2+5x-4

extreme points

f (x) = - x^{3} - x^{2} + 5 x - 4

Minimum (- \frac{5}{3}, - \frac{283}{27}), Maximum (1, - 1)

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 - 4 : - \frac{283}{27}

Minimum (- \frac{5}{3}, - \frac{283}{27})

Plug

x = 1

into

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

Maximum (1, - 1)

Minimum (- \frac{5}{3}, - \frac{283}{27}), Maximum (1, - 1)

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

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

- x^{2} + 10 x + 25

f (x) = 4 x^{3} - 440 x^{2} + 10500 x

f (x) = 4 + 15 x + 6 x^{2} - x^{3}

What is the extreme f(x)=-x^3-x^2+5x-4 ?
The extreme f(x)=-x^3-x^2+5x-4 is Minimum(-5/3 ,-283/27),Maximum(1,-1)