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

The extreme f(x)= 1/3 x^3-x^2-3x+3 is Maximum(-1, 14/3),Minimum(3,-6)

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

extreme points

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

Maximum (- 1, \frac{14}{3}), Minimum (3, - 6)

Solution steps

f^{'} (x) = x^{2} - 2 x - 3

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 1

into

\frac{1}{3} x^{3} - x^{2} - 3 x + 3 : \frac{14}{3}

Maximum (- 1, \frac{14}{3})

Plug

x = 3

into

\frac{1}{3} x^{3} - x^{2} - 3 x + 3 : - 6

Minimum (3, - 6)

Maximum (- 1, \frac{14}{3}), Minimum (3, - 6)

f (x) = 5 x^{3} - 30 x^{2} + 45 x

f (x) = x y^{2} - 6 x^{2} - 3 y^{2}

f (x) = 3 x + \frac{1}{x}

f (x) = x^{3} - 15 x^{2} + 48 x + 2

\frac{x ^{2} - 5}{x + 3}

What is the extreme f(x)= 1/3 x^3-x^2-3x+3 ?
The extreme f(x)= 1/3 x^3-x^2-3x+3 is Maximum(-1, 14/3),Minimum(3,-6)