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Let f:R to R be a function satisfying f(...

Let `f:R to R` be a function satisfying `f(x+y)=f(x)=lambdaxy+3x^(2)y^(2)"for all "x,y in R`
If f(3)=4 and f(5)=52, then f'(x) is equal to

A

`10x`

B

`-10x`

C

`20x`

D

`128x`

Text Solution

Verified by Experts

The correct Answer is:
B
Put x = x, y = h
`f(x+h)-f(x)=lambdaxh+3x^(2)h^(2)`
`therefore" "underset(hrarr0)(lim)(f(x+h)-f(x))/(h)=lambdax`
`therefore" "f'(x)=lambdax`
Putting x = 3, y = 2
`therefore" "f(5)=f(3)+lambda(6)+3(3)^(2)(2)^(2)`
`therefore" "48+6lambda+108`
`rArr" "lambda=-10`
`" "f'(x)=-10x`
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