Barrons AP Calculus - David Bock

(C) Let the tangent to the parabola from (3, 5) meet the curve at (x 1 , y 1 ). Its equation is y − 5 =
2 x 1 (x − 3). Since the point (x 1 , y 1 ) is on both the tangent and the parabola, we solve
simultaneously:
y 1 − 5 = 2x 1 (x 1 − 3) and
The points of tangency are (5, 25) and (1, 1). The slopes, which equal 2x 1 , are 10 and 2.