Q.

The minimum area bounded by the function 
y=⨍ (x) and y=αx+9(αR) where ⨍ (x) satisfies the relation ⨍ (x+y)=⨍ (x)+⨍ (y)+y⨍ (x)∀x, γ∈R and ⨍ 1(0)=0 is 9A. value of A is _______

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answer is 8.

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Detailed Solution

f'x=limh0fx+h-fxh=limh0fh+hfxh

f'x=f'(0)+fxf'x=fx

f'xfxdx=dx2fx=x

fx=x24

If α=0 Area is minimum

 

Required minimum area =2092ydy=83y3209=8327=72 9A=72A=8 

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