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

The extreme f(x)=-x^3-x^2+5x is Minimum(-5/3 ,-175/27),Maximum(1,3)

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

extreme points

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

Minimum (- \frac{5}{3}, - \frac{175}{27}), Maximum (1, 3)

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 : - \frac{175}{27}

Minimum (- \frac{5}{3}, - \frac{175}{27})

Plug

x = 1

into

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

Maximum (1, 3)

Minimum (- \frac{5}{3}, - \frac{175}{27}), Maximum (1, 3)

f (x) = x^{5} - 5 x^{4}

f (x) = x - y

f (x, y) = x y + 5 x - 5

f (x) = x + \frac{1}{x}, 0.2 \leq x \leq 4

f (x, y) = x^{3} + 3 x y^{2} - 3 y^{2} - 3 x^{2} + 11

What is the extreme f(x)=-x^3-x^2+5x ?
The extreme f(x)=-x^3-x^2+5x is Minimum(-5/3 ,-175/27),Maximum(1,3)