en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=(100-2x)(75-2x)x

Solution

extreme points

f (x) = (100 - 2 x) \cdot (75 - 2 x) \cdot x

Solution

Maximum (\frac{25 ( 7 - 13 )}{6}, \frac{15625 ( 35 + 13 13 )}{27}), Minimum (\frac{25 ( 7 + 13 )}{6}, \frac{15625 ( 35 - 13 13 )}{27})

Solution steps

f^{'} (x) = 4 (3 x^{2} - 175 x + 1875)

Find intervals:

Increasing

: - \infty < x < \frac{- 25 13 + 175}{6},

Decreasing

: \frac{- 25 13 + 175}{6} < x < \frac{25 13 + 175}{6},

Increasing

: \frac{25 13 + 175}{6} < x < \infty

Plug

x = \frac{25 ( 7 - 13 )}{6}

into

(100 - 2 x) \cdot (75 - 2 x) \cdot x : \frac{15625 ( 35 + 13 13 )}{27}

Maximum (\frac{25 ( 7 - 13 )}{6}, \frac{15625 ( 35 + 13 13 )}{27})

Plug

x = \frac{25 ( 7 + 13 )}{6}

into

(100 - 2 x) \cdot (75 - 2 x) \cdot x : \frac{15625 ( 35 - 13 13 )}{27}

Minimum (\frac{25 ( 7 + 13 )}{6}, \frac{15625 ( 35 - 13 13 )}{27})

Maximum (\frac{25 ( 7 - 13 )}{6}, \frac{15625 ( 35 + 13 13 )}{27}), Minimum (\frac{25 ( 7 + 13 )}{6}, \frac{15625 ( 35 - 13 13 )}{27})

Popular Examples

extreme f(x)=5xsqrt(x-x^2)extreme points

f (x) = 5 x x - x^{2}

extreme f(x)=x^2-72ln(x)extreme points

f (x) = x^{2} - 72 ln (x)

extreme f(x)=x^{(2/3)}extreme points

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

extreme f(x)=((x+4))/(x^2-3x-28)extreme points

f (x) = \frac{( x + 4 )}{x ^{2} - 3 x - 28}

extreme f(x,y)=3x+5y+2 extreme points

f (x, y) = 3 x + 5 y + 2

Frequently Asked Questions (FAQ)

What is the extreme f(x)=(100-2x)*(75-2x)*x ?
The extreme f(x)=(100-2x)*(75-2x)*x is