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Question

What is/are the tangents to y=(x31)(x2) at the points where the curve cuts the x-axis

A
y+3x=3
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B
y+2x=3
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C
y7x+14=0
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D
y5x14=0
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Solution

The correct options are
A y+3x=3
C y7x+14=0
Given curve is, y=(x31)(x2)
For intersection of this curve with x-axis put y=0
(x31)(x2)=0x=1,2
Thus points are (1,0) and (2,0)
Now dydx=(x31)+(x2).3x2=4x36x21
So slope of the tangent are m1=(dydx)x=1=3 and m2=(dydx)x=2=7
Hence required tangents are, y+3x=3,y7x+14=0

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