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For y = f(x) = into^x 2|t| dt, the tang...

For `y = f(x) = int_o^x 2|t| dt`, the tangent lines parallel to the bisector of the first quadrant angle are (A) `y= x pm 1/4` (B) ` y = x pm 3/2` (C) `y= x pm 1/2` (D) None of these

Text Solution

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`y=f(x)=int_0^x2|t|dt`
`f(x)=int_0^x 2tdt=x^2`
`f(x)=int_0^x -2tdt=-x^2`
When m=1
x>0 `f'(x)=2x=1,x=1/2`
x<0 `f'(x)=-2x=1,x=-1/2`
`y=x^2=1/4`
`P(1/2,1/4)`
...
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