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

The extreme f(x)=x^3+x^2-x+2 is Maximum(-1,3),Minimum(1/3 , 49/27)

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

extreme points

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

Maximum (- 1, 3), Minimum (\frac{1}{3}, \frac{49}{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 + 2 : 3

Maximum (- 1, 3)

Plug

x = \frac{1}{3}

into

x^{3} + x^{2} - x + 2 : \frac{49}{27}

Minimum (\frac{1}{3}, \frac{49}{27})

Maximum (- 1, 3), Minimum (\frac{1}{3}, \frac{49}{27})

f (x, y) = \frac{y}{x + y ^{3}}

f (x, y) = x^{3} + 12 x y^{2} - 15 x - 24 x

f (x) = sin (x) - cos^{2} (x), 0 \leq x \leq 2 π

f (x, y) = e^{x^{2} - y^{2}}

f (x) = 8 x - \frac{8 x ^{2}}{2} - x y^{2} + \frac{8 y ^{2}}{16} + 7

What is the extreme f(x)=x^3+x^2-x+2 ?
The extreme f(x)=x^3+x^2-x+2 is Maximum(-1,3),Minimum(1/3 , 49/27)