Question 3.2 #51
The key to this question is to try to calculate the slope of the tangent in two
Given a tangent line that passes though he poit (1,2), suppose that it
touches the curve at the point of tangency a,a+1 . Our goal is to ﬁnd what
a could be.
Let’s calculate the slope of the tangent at x = a on the curve in two ways.
• First, we have the correspondence that the slope of the tangent at x = a
is the derivative y (a).
0 (x+1)−x 1
y (x) = (x+1)2 = (x+1)2
y (a) = (a+1)
• Scond, emember that two points on the tangent line are (1,2) and