What is the extreme f(x)= 1/6 x^3-x^2-6x+11 ?

The extreme f(x)= 1/6 x^3-x^2-6x+11 is Maximum(-2, 53/3),Minimum(6,-25)

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extreme f(x)= 1/6 x^3-x^2-6x+11

extreme points

f (x) = \frac{1}{6} x^{3} - x^{2} - 6 x + 11

Maximum (- 2, \frac{53}{3}), Minimum (6, - 25)

Solution steps

f^{'} (x) = \frac{x ^{2}}{2} - 2 x - 6

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = - 2

into

\frac{1}{6} x^{3} - x^{2} - 6 x + 11 : \frac{53}{3}

Maximum (- 2, \frac{53}{3})

Plug

x = 6

into

\frac{1}{6} x^{3} - x^{2} - 6 x + 11 : - 25

Minimum (6, - 25)

Maximum (- 2, \frac{53}{3}), Minimum (6, - 25)

f (x) = \frac{ln ( x )}{5 x}, 1 \leq x \leq 4

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

Q (x, y) = x y

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

f (x) = (8 - 4 x)^{8}

What is the extreme f(x)= 1/6 x^3-x^2-6x+11 ?
The extreme f(x)= 1/6 x^3-x^2-6x+11 is Maximum(-2, 53/3),Minimum(6,-25)