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

The extreme g(x)=x^3-x^2-x+3 is Maximum(-1/3 , 86/27),Minimum(1,2)

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extreme g(x)=x^3-x^2-x+3

extreme

Maximum (- \frac{1}{3}, \frac{86}{27}), Minimum (1, 2)

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 + 3 : \frac{86}{27}

Maximum (- \frac{1}{3}, \frac{86}{27})

Plug

x = 1

into

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

Minimum (1, 2)

Maximum (- \frac{1}{3}, \frac{86}{27}), Minimum (1, 2)

What is the extreme g(x)=x^3-x^2-x+3 ?
The extreme g(x)=x^3-x^2-x+3 is Maximum(-1/3 , 86/27),Minimum(1,2)