Cracking The Ap Calculus ab Exam 2018

= −3 − 2(2) = −7

Third, plug the slope and the point into the equation for the line.

y   −   (−6)    =   −7  (x  −   2)

This simplifies to y = −7x + 8.

PROBLEM 2. Find the equation of the normal line to the graph of y = 6 − x − x^2 at x = −1.

Answer: Plug x = −1 into the original equation to get the y-coordinate.

y   =   6   +   1   −   1   =   6

Once again, take that derivative.

    =   −1  −   2x

Now plug in x = −1 to get the slope of the tangent.

= −1 − 2(−1)=1

Use the negative reciprocal of the slope in the second step to get the slope of the normal line.

m   =   −1

Finally, plug the slope and the point into the equation for the line.

y   −   6   =   −1  (x  +   1)

This simplifies to y = −x + 5.

PROBLEM 3. Find the equations of the tangent and normal lines to the graph of y = at the point (2,

4).

Answer: This problem will put your algebra to the test. You have to use the Quotient Rule to take the
derivative of this mess.