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Popular >

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

Solution

extreme points

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

Solution

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

Solution steps

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

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

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

Plug

x = 0

into

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

Minimum (0, 0)

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

Popular Examples

extreme f(x,y)=x^3+y^2-2xy+7x-8y+2 extreme points

f (x, y) = x^{3} + y^{2} - 2 x y + 7 x - 8 y + 2

extreme f(x,y)=e^{x^2+y^2+1}extreme points

f (x, y) = e^{x^{2} + y^{2} + 1}

extreme F(x)=x^3-6x^2+9x+15 extreme points

F (x) = x^{3} - 6 x^{2} + 9 x + 15

extreme f(x)=x^2y+xy^2+3xy extreme points

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

extreme f(x)=((x-3)(x+3)^2)/(2(x+1)^3)extreme points

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

Frequently Asked Questions (FAQ)

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