logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  CBSE XII  >>  Math  >>  Application of Derivatives
0 votes

Find two positive numbers \(x\) and \(y\) such that their sum is 35 and the product \(x^2 y^5\) is a maximum.

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • $\large\frac{d}{dx}$$(x^n)=na^{n-1}$
Step 1:
$x+y=35$
$y=35-x$
$P=x^2y^5$
$P=x^2(35-x)^5$
$\large\frac{dP}{dx}$$=x^2.5(35-x)^4(-1)+(35-x)^5.2x$
$\quad\;=x^2(35-x)^4[-5x+2(35-x)]$
$\quad\;=x^2(35-x)^4[70-7x]$
Step 2:
When $x$ is slightly < 10 $\large\frac{dP}{dx}=$$(+)(+)(+)=+ve$
When $x$ is slightly > 10 $\large\frac{dP}{dx}=$$(+)(+)(-)=-ve$
$\Rightarrow \large\frac{dP}{dx}$ changes sign from +ve to -ve as $x$ increases through 10.
$\Rightarrow P$ is maximum at $x=10$
From (1) $y=35-10=25$
Hence the required numbers are 10 & 25.
answered Aug 8, 2013 by sreemathi.v
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...