Ask Questions, Get Answers

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

Find two numbers whose sum is 24 and whose product is as large as possible.

Can you answer this question?

1 Answer

0 votes
  • $\large\frac{d}{dx}\big(x^n)=nx^{n-1}$
  • For maximum value $\large\frac{dP}{dx}$$=0$
Step 1:
Sum of two no$\rightarrow$ 24
Product $\rightarrow$ as large as possible
Let the required number be $x$ and $(24-x)$
Their product $P=x(24-x)$
Step 2:
For maximum value
Now $\large\frac{dP}{dx}$$=0$
Differentiating with respect to x we get
$\large\frac{d^2P}{dx^2}$$=-2 < 0$
$\Rightarrow P$ is minimum at $x=12$
Hence the required numbers are 12 and $(24-12)\Rightarrow (i.e)12$
answered Aug 8, 2013 by sreemathi.v
edited Aug 19, 2013 by sharmaaparna1

Related questions

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