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Popular >

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

Solution

extreme points

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

Solution

Maximum (- \frac{2}{3}, \frac{4}{27}), Minimum (0, 0)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - \frac{2}{3},

Decreasing

: - \frac{2}{3} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{2}{3}

into

x^{3} + x^{2} : \frac{4}{27}

Maximum (- \frac{2}{3}, \frac{4}{27})

Plug

x = 0

into

x^{3} + x^{2} : 0

Minimum (0, 0)

Maximum (- \frac{2}{3}, \frac{4}{27}), Minimum (0, 0)

Popular Examples

extreme f(x)=2x^5+5x^4-15 extreme points

f (x) = 2 x^{5} + 5 x^{4} - 15

asymptotes of f(x)=(x-1)/((x+3)(x-1))asymptotes

f (x) = \frac{x - 1}{( x + 3 ) ( x - 1 )}

distance (5,-2),(-7,3)distance

(5, - 2), (- 7, 3)

asymptotes of f(x)=(24x^2+6x)/(2x+1)asymptotes

f (x) = \frac{24 x ^{2} + 6 x}{2 x + 1}

range of f(x)=sqrt(x^2+2x-15)range

f (x) = x^{2} + 2 x - 15

Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^3+x^2 ?
The extreme f(x)=x^3+x^2 is Maximum(-2/3 , 4/27),Minimum(0,0)