Barrons AP Calculus - David Bock

For BC Calculus students, this chapter reviewed finding slopes of curves defined parametrically
or in polar form. We have also reviewed the use of vectors to describe the position, velocity, and
acceleration of objects in motion along curves.

Practice Exercises

Part A. Directions: Answer these questions without using your calculator.

1. The slope of the curve y^3 − xy^2 = 4 at the point where y = 2 is
   (A) −2
   (B)
   (C)
   (D)
   (E) 2


2. The slope of the curve y^2 − xy − 3x = 1 at the point (0, −1) is
   (A) −1
   (B) −2
   (C) +1
   (D) 2
   (E) −3


3. The equation of the tangent to the curve y = x sin x at the point is
   (A) y = x − π
   (B)
   (C) y = π − x
   (D)
   (E) y = x


4. The tangent to the curve of y = xe−x is horizontal when x is equal to
   (A) 0
   (B) 1
   (C) −1
   (D)
   (E) none of these