en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme (x^2)/(x+3)

Solution

extreme points

\frac{x ^{2}}{x + 3}

Solution

Maximum (- 6, - 12), Minimum (0, 0)

Solution steps

f^{'} (x) = \frac{x ^{2} + 6 x}{( x + 3 ) ^{2}}

Find intervals:

Increasing

: - \infty < x < - 6,

Decreasing

: - 6 < x < - 3,

Decreasing

: - 3 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 6

into

\frac{x ^{2}}{x + 3} : - 12

Maximum (- 6, - 12)

Plug

x = 0

into

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

Minimum (0, 0)

Maximum (- 6, - 12), Minimum (0, 0)

Popular Examples

extreme f(x)=sin(4x),0<= x<= pi/2 extreme points

f (x) = sin (4 x), 0 \leq x \leq \frac{π}{2}

extreme f(x)=xsqrt(x^2+4)extreme points

f (x) = x x^{2} + 4

extreme f(x)=2x^3-24x^2+72x+5 extreme points

f (x) = 2 x^{3} - 24 x^{2} + 72 x + 5

extreme f(x)=2+54x-2x^3 extreme points

f (x) = 2 + 54 x - 2 x^{3}

extreme f(x,y)=sqrt(4+2x-4y-x^2-y^2)extreme points

f (x, y) = 4 + 2 x - 4 y - x^{2} - y^{2}

Frequently Asked Questions (FAQ)

What is the extreme (x^2)/(x+3) ?
The extreme (x^2)/(x+3) is Maximum(-6,-12),Minimum(0,0)