Cracking The Ap Calculus ab Exam 2018

y   +       =   − (x    −   1), or  2   y   =   −9x +   2

Sometimes, instead of finding the equation of a tangent line, you will be asked to find the equation of a
normal line. A normal line is simply the line perpendicular to the tangent line at the same point. You
follow the same steps as with the tangent line, but you use the slope that will give you a perpendicular
line.

Remember:   The slope   of  a   perpendicular   line    is  just    the

negative    reciprocal  of  the slope   of  the tangent line.

Example 4: Find the equation of the line normal to y = x^5 − x^4 + 1 at x = 2.

First, find the y-coordinate.

y   (2) =   2^5     −   2^4     +   1   =   17

Second, take the derivative.

    =   5x^4    −   4x^3

Third, find the slope at x = 2.

= 5(2)^4 − 4(2)^3 = 48

Fourth, take the negative reciprocal of 48, which is − .

Finally, the equation becomes

y   −   17  =   −    (x −   2)

Try these solved problems. Do each problem, covering the answer first, then checking your answer.

PROBLEM 1. Find the equation of the tangent line to the graph of y = 4 − 3x − x^2 at the point (2, −6).

Answer: First, take the derivative of the equation.

    =   −3  −2x

Now, plug in x = 2 to get the slope of the tangent line.