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Question

If the line joining the points (0,3) and (5,−2) is the tangent to the curve y=cx+1 then the value of c is

A
1
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B
2
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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
Slop of line joining the points (0,3)and(5,2) is given by
3+205=1

This is equal to the slop of tangent on the curve and that is given by

dydx=c(x+1)2dydx=1c=(x+1)2...................(1)\

Equation of line joining the points (0,3)and(5,2) is given by

(y3)=1(x0)

Solving equation of tangent and the curve for point of intersection

cx+1+x=3.............(2)

Solving (1) and (2)

x=1

Putting this in (2), we get c=4

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