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Question

The triangle formed by the tangent to the curve f(x)=x2+bx-bat the point (1,1) and the coordinate axes lie in the first quadrant. If its area is 2, then the value of b is


A

-1

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B

3

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C

-3

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D

1

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Solution

The correct option is C

-3


Explanation for correct option :

Let y=fx

Given f(x)=x2+bx-b

m=dydxm=ddxx2+bx-bm=2x+b

The equation of the tangent at (1,1)

y-y1=mx-x1y-1=b+2x-1y-1=bx-b+2x-2y-xb+2+b+1=0

We know that Area of triangle =12×base×height

2=12×b+1b+2×-b+14b+8=-b2-2b-1b2+6b+9=0b+32=0b=-3

Hence Option(C) is the answer.


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