Review for Chapter 3 Test
Topics on the Test
1
2
3
Find the equation of a tangent line and/or normal line (of an explicit or implicit equation)
Find and simplify first and second derivatives (using the various rules)
Use product and quotient rules (example: if f(3) = 4, f’(3) = 5, g(3) = -1 and g’(3) = 2, what is the
derivative of f(3)g(3)?)
4 Implicit differentiation
5 Derivatives of logarithmic and inverse trig functions
6 Logarithmic differentiation
7 Linear approximation
8 Using a differential to estimate errors
9 Position, velocity, acceleration problems (section 3.8)
10 Prove one or more of the following derivative rules: one of the 6 trigonometric functions; log or
ln (using implicit differentiation); power, product or quotient rule (using logarithmic
differentiation); inverse sin, cos or tan (using implicit differentiation)
The following formulas will be provided:
1
2
Derivatives of inverse trigonometric functions
Linear approximation
Be sure to remember:
1
2
3
4
Derivatives of trigonometric, logarithmic, exponential functions
Product, quotient, and chain rule
Rules for logarithms
If and only if 2 lines are perpendicular, then the slopes are opposite reciprocals
Sample Questions
1) Given the function f(x) = ln(3x2 – 5x), find the equation of the normal line at the point where x = 2
2) Given the curve 4x2y – 8x = –12y,
a) Find
dy
dx
b) Find the slope of the tangent line at the point (1, 1/2)
3) Use logarithmic differentiation to find dy/dx:
y
x4 x  1
6x  5
4) Given the function f(x) =
3
x
a) Find the linear approximation of the function for a = 2
b) Use the linear approximation you found in part (a) to estimate
3
2.05
5) Find the derivative of y  sin 1 (4 x)
6) If f(3) = 4, f '(3) = -2, g(3) = -2 and g '(3) = 5, then compute the derivative of f(3)g(3)
7) A cylinder has a radius of 10 cm and a height of 15 cm. The margin of error or the radius is 0.5 cm.
What is the margin of error for the volume of the cylinder? Use the formula V   r 2 h
8) Use logarithmic differentiation to prove the product rule
Additional practice questions from the textbook (pages 248-250): 1-46, 52, 68, 70, 75a, 76