Mathematics

Problem

For the parabola

y = x^2

, consider the points

P(-1,1)

and

Q(2,4)

on the curve. a. (i) Find the slopes of the tangents to the curve at

P

and

Q

. b. (ii) Obtain the equations of these two tangents. c. (iii) Calculate the acute angle between the two tangents at the points

P

and

Q