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if x+y=10, thent he maximum value of xy ...

if `x+y=10`, thent he maximum value of xy is

A

5

B

20

C

25

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`x+y=10,becausey=10-x` ..(i)
Now `f(x)=xy=x(10-x)=10x-x^(2)`
`becausef^(`)(x)=(10-2x)`
For maximum value of `f(x),f^(`)(x)=0`
`x=5` and `y=5`
So maximum value of `xy=5xx=25`.
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