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

The extreme f(x)=x^3-x^2-x+6 is Maximum(-1/3 , 167/27),Minimum(1,5)

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

extreme points

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

Maximum (- \frac{1}{3}, \frac{167}{27}), Minimum (1, 5)

Solution steps

f^{'} (x) = 3 x^{2} - 2 x - 1

Find intervals:

Increasing

: - \infty < x < - \frac{1}{3},

Decreasing

: - \frac{1}{3} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - \frac{1}{3}

into

x^{3} - x^{2} - x + 6 : \frac{167}{27}

Maximum (- \frac{1}{3}, \frac{167}{27})

Plug

x = 1

into

x^{3} - x^{2} - x + 6 : 5

Minimum (1, 5)

Maximum (- \frac{1}{3}, \frac{167}{27}), Minimum (1, 5)

x 6 - x

f (x) = x e^{\frac{2}{x}}

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

f (x) = 2 x^{3} - 4 x^{2} + 2 x + 1

4 - 3 x - x^{3}

What is the extreme f(x)=x^3-x^2-x+6 ?
The extreme f(x)=x^3-x^2-x+6 is Maximum(-1/3 , 167/27),Minimum(1,5)