Math 117
Test 1 Review
Topics
Chapter 10
Limit of a function as x  a .
Limit of the difference quotient as h  0 .
Continuity: Find the points of discontinuity such as where
(1) f(x) is undefined because the denominator is 0 or
(2) for case-defined function, the points where you change cases.
Example: f ( x)  10 x  x 2 for x < 5
2
for x  5
Inequalities: A function (the y value) can change from positive
( f ( x)  0) to negative ( f ( x)  0) when f ( x)  0 or at a point of
discontinuity such as where f(x) is undefined.
Chapter 11
dy
Definition of the derivative, f (x) or
, as the limit of the difference
dx
quotient as h approaches 0. Find the derivative using the definition
for linear or quadratic functions.
Find the derivative using short-cut rules (11.2), product and quotient
rules (11.4), and chain rule (11.5).
Interpretation of the derivative:
(1) f (x) gives the slope of the graph at x which is the slope of
the tangent line.
(2)
dy
gives the rate of change in y with respect to x at a point.
dx
(3) Understand the difference between the slope of the secant
line from x to x+1 and the slope of the tangent line at x
Applications:
Be able to find marginal cost and explain what it represents.
Understand the difference between marginal cost and average
cost.
Be able to find marginal revenue and explain what it represents
given a demand function.
Be able to find the rate of change for any function and explain
its meaning including units.
Use the chain rule to find rates of change in a two step process.