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(25-39+2x)(39/2-x)

Solution

extreme points

f (x) = x (25 - 39 + 2 x) (\frac{39}{2} - x)

Solution

Minimum (\frac{53 - 1171}{6}, \frac{18656 - 1171 1171}{54}), Maximum (\frac{53 + 1171}{6}, \frac{1171 1171 + 18656}{54})

Solution steps

f^{'} (x) = - 6 x^{2} + 106 x - 273

Find intervals:

Decreasing

: - \infty < x < \frac{- 1171 + 53}{6},

Increasing

: \frac{- 1171 + 53}{6} < x < \frac{1171 + 53}{6},

Decreasing

: \frac{1171 + 53}{6} < x < \infty

Plug

x = \frac{53 - 1171}{6}

into

x (25 - 39 + 2 x) (\frac{39}{2} - x) : \frac{18656 - 1171 1171}{54}

Minimum (\frac{53 - 1171}{6}, \frac{18656 - 1171 1171}{54})

Plug

x = \frac{53 + 1171}{6}

into

x (25 - 39 + 2 x) (\frac{39}{2} - x) : \frac{1171 1171 + 18656}{54}

Maximum (\frac{53 + 1171}{6}, \frac{1171 1171 + 18656}{54})

Minimum (\frac{53 - 1171}{6}, \frac{18656 - 1171 1171}{54}), Maximum (\frac{53 + 1171}{6}, \frac{1171 1171 + 18656}{54})

Graph

Popular Examples

extreme f(x)=x^2+8x+11 extreme points

f (x) = x^{2} + 8 x + 11

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

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

extreme f(x)=-sqrt(9-x^2),-2<= x<= 3 extreme points

f (x) = - 9 - x^{2}, - 2 \leq x \leq 3

extreme f(y)=x^3-9x^2+7x-6 extreme points

f (y) = x^{3} - 9 x^{2} + 7 x - 6

extreme sin(3x),-pi/4 <= x<= pi/3 extreme points

sin (3 x), - \frac{π}{4} \leq x \leq \frac{π}{3}

Frequently Asked Questions (FAQ)

What is the extreme f(x)=x(25-39+2x)(39/2-x) ?
The extreme f(x)=x(25-39+2x)(39/2-x) is