Find parameter p so that y = 3x is a tangent line to the curve y = x 2 + p

Question

SAGAR SINGH - IIT DELHI · Answer

Dear nitin,

The slope of the tangent is equal to 3. At the point of tangency y ' = 3.

y ' = 2 x = 3

Solve the equation 2 x = 3 to find the x coordinate of the point of tangency.

x = 3 / 2

The point of tangency is on the line y = 3 x, therefore the y coordinate of the point of tangency is equal to

y = 3 (3/2) = 9 / 2

The point of tangency (3 / 2 , 9 / 2) is on the curve
y = x² + p and is therefore used to find p as follows

9 / 2 = (3 / 2)² + p

Solve the above for p to obtain

p = 9 / 4

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Sagar Singh

B.Tech IIT Delhi

Find parameter p so that y = 3x is a tangent line to the curve
y = x² + p