What is the extreme f(x)=(x^3)/3-x^2-15x ?

The extreme f(x)=(x^3)/3-x^2-15x is Maximum(-3,27),Minimum(5,-175/3)

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extreme f(x)=(x^3)/3-x^2-15x

extreme points

f (x) = \frac{x ^{3}}{3} - x^{2} - 15 x

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

Solution steps

f^{'} (x) = x^{2} - 2 x - 15

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = - 3

into

\frac{x ^{3}}{3} - x^{2} - 15 x : 27

Maximum (- 3, 27)

Plug

x = 5

into

\frac{x ^{3}}{3} - x^{2} - 15 x : - \frac{175}{3}

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

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

f (x, y) = x^{2} - x y + y^{2} + 9 x - 6 y + 10

f (x, y) = x^{2} y + y^{3} - 48 y

f (x) = - 5 x^{4} - 5 x^{3} + 29

f (x) = 7 sin (x) + 7 cos (x), 0 \leq x \leq 2 π

x^{3} - 6 x^{2} + 1

What is the extreme f(x)=(x^3)/3-x^2-15x ?
The extreme f(x)=(x^3)/3-x^2-15x is Maximum(-3,27),Minimum(5,-175/3)