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The two parts of 100 for which the sum o...

The two parts of 100 for which the sum of double of first and square of second part is minimum, are a. 50,50 b. 99,1 c. 98,2 d. none of these

A

50,50

B

99,1

C

98,2

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let one number bet `(100-x)` and then another is `x`.
Therefore `f(x)=2(100-x)+x^(2)`
`=x^(2)-2x+200`
For minimum put `f'(x)=0implies2x-2=0impliesx=1`
Here `f''(x)=2gt0`
Therefore, function is minimum at `x=1`
So, the numbers are 99 and 1.
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