Applications Of Derivatives Question 357
Question: The two parts of 100 for which the sum of double of first and square of second part is minimum, are
Options:
A) 50, 50
B) 99, 1
C) 98, 2
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Let one number is $ (100-x) $ and then another is x. Therefore $ f(x)=2(100-x)+x^{2}=x^{2}-2x+200 $
$ f’(x)=0\Rightarrow 2x-2=0\Rightarrow x=1 $
Here $ {f}’’,(x)=2>0 $ Therefore function is minimum at $ x=1 $ So the numbers are 99 and 1.
BETA
