Course:MATH110/Archive/2010-2011/003/Lectures/Lecture 51

Here's a typical calculus problem:

Problem

Consider the tangent line to the parabola $y=x^{2}$ at the point ($a$,$a^{2}$). Find the equation to the line which is perpendicular to that line and passes through the point ($a$,$a^{2}$).

Below are two solutions provided by some students. Evaluate each solution, if you find mistakes, explain where they occurred and what caused them. Then provide some suggestions to help the student understand what went wrong.

First solution

Second solution