Remember two lines are perpendicular to one another if and only if their slopes are negative reciprocals of each other.Originally Posted by compuryan
Thus, means the perpendicular line has slope .
The slope of any given point on the graph is its derivative which is,
We need that to be as explained in the first paragraph thus, . Solving we have that . These are the two x-values on the graph where the tangent is perpendicular to this line.