Applications Of Derivatives Question 323
Question: The sum of two numbers is fixed. Then its multiplication is maximum, when
Options:
A) Each number is half of the sum
B) Each number is $ \frac{1}{3} $ and $ \frac{2}{3} $ respectively of the sum
C) Each number is $ \frac{1}{4} $ and $ \frac{3}{4} $ respectively of the sum
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Suppose that two numbers are $ x $ and $ y $ .
$ x+y=s\Rightarrow y=s-x $
Then $ f(x)=xy=x(s-x)=xs-x^{2} $
$ \therefore f’(x)=s-2x $
$ f’(x)=0 $ for maximum value of $ f(x) $
$ \therefore x=\frac{s}{2} $ and $ y=\frac{s}{2} $
Thus each number is half of the sum.
BETA
