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Question

The slope of the tangents to the curve y=(x+1)(x3) at the points where it crosses x - axis are

A
±2
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B
±3
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C
±4
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D
None of these
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Solution

The correct option is A ±4
y=(x+1)(x3)..(1)

Substitute y=0 to get the point of intersection of this curve with xaxis

0=(x+1)(x3)

x=1,3

So the points are (1,0) and (3,0)

Now differentiating eq. (1), we get

dydx=(x3)+(x+1)=2x2

(dydx)=2(x1)

Thus slope at (1,0) is =(dydx)(1,0)=4

and at (3,0) is =(dydx)(3,0)=4

Hence, option 'C' is correct.

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