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

The extreme f(x)=x^3+x^2-x+3 is Maximum(-1,4),Minimum(1/3 , 76/27)

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

extreme

Maximum (- 1, 4), Minimum (\frac{1}{3}, \frac{76}{27})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

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

Increasing

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

Plug

x = - 1

into

x^{3} + x^{2} - x + 3 : 4

Maximum (- 1, 4)

Plug

x = \frac{1}{3}

into

x^{3} + x^{2} - x + 3 : \frac{76}{27}

Minimum (\frac{1}{3}, \frac{76}{27})

Maximum (- 1, 4), Minimum (\frac{1}{3}, \frac{76}{27})

What is the extreme f(x)=x^3+x^2-x+3 ?
The extreme f(x)=x^3+x^2-x+3 is Maximum(-1,4),Minimum(1/3 , 76/27)