en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=x(16-39+2x)(39/2-x)

Solution

extreme points

f (x) = x (16 - 39 + 2 x) (\frac{39}{2} - x)

Solution

Minimum (\frac{62 - 1153}{6}, - \frac{11935 + 1153 1153}{54}), Maximum (\frac{62 + 1153}{6}, \frac{1153 1153 - 11935}{54})

Solution steps

f^{'} (x) = - 6 x^{2} + 124 x - \frac{897}{2}

Find intervals:

Decreasing

: - \infty < x < - \frac{1153}{6} + \frac{31}{3},

Increasing

: - \frac{1153}{6} + \frac{31}{3} < x < \frac{1153}{6} + \frac{31}{3},

Decreasing

: \frac{1153}{6} + \frac{31}{3} < x < \infty

Plug

x = \frac{62 - 1153}{6}

into

x (16 - 39 + 2 x) (\frac{39}{2} - x) : - \frac{11935 + 1153 1153}{54}

Minimum (\frac{62 - 1153}{6}, - \frac{11935 + 1153 1153}{54})

Plug

x = \frac{62 + 1153}{6}

into

x (16 - 39 + 2 x) (\frac{39}{2} - x) : \frac{1153 1153 - 11935}{54}

Maximum (\frac{62 + 1153}{6}, \frac{1153 1153 - 11935}{54})

Minimum (\frac{62 - 1153}{6}, - \frac{11935 + 1153 1153}{54}), Maximum (\frac{62 + 1153}{6}, \frac{1153 1153 - 11935}{54})

Graph

Popular Examples

extreme 6x-7x^{6/7}extreme points

6 x - 7 x^{\frac{6}{7}}

extreme f(x)=-x^{2/3}(x-5),-5<= x<= 5 extreme points

f (x) = - x^{\frac{2}{3}} (x - 5), - 5 \leq x \leq 5

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

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

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

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

extreme 14x^2-2x^3+2y^2+4xy extreme points

14 x^{2} - 2 x^{3} + 2 y^{2} + 4 x y

Frequently Asked Questions (FAQ)

What is the extreme f(x)=x(16-39+2x)(39/2-x) ?
The extreme f(x)=x(16-39+2x)(39/2-x) is