Survey of Calculus Spring 2017

Survey of Calculus Spring 2017

Test #1 Review:

SectionKey Skills

2.1 Find an average rate of change

--algebraically, graphically, or numerically

 Understand average rate of change

--slope of secant line, notation, units, interpretation

2.2 Find a limit

--algebraically, graphically, or numerically

2.3 Find an instantaneous rate of change

--algebraically, graphically, or numerically

 Understand instantaneous rate of change

--slope of tangent line, notation, units, interpretation

2.4 Find a derivative function algebraically

--find the equation of a tangent line to a function at a point

 Find a derivative function graphically

--interpret a first or second derivative graphically

Test #2 Review:

SectionKey Skills

3.1, 3.5 Calculate a derivative using the power, constant multiple, sum

and difference, exponential, or logarithmic rule

 Find the equation of a tangent line to a function at a point

 Calculate and interpret a second derivative

3.3 Calculate a derivative using the product or quotient rule

--algebraically, graphically, or numerically

 Find the equation of a tangent line to a function at a point

Test #3 Review:

SectionKey Skills

3.4 Calculate a derivative using the chain rule

--algebraically, graphically, or numerically

 Calculate a derivative using the exponential or logarithmic rule

with any base

 Find the equation of a tangent line to a function at a point

3.5 Calculate a derivative using implicit differentiation

3.6 Use an exponential model to describe and find rates of change of

financial, population, physical, or biological growth or decay

Test #4 Review:

SectionKey Skills

4.2, 4.3 Find absolute and local minimums and maximums algebraically

 Calculate features of a function based on the first and second

derivatives

--increasing/decreasing, local max/min, concave up/down,

inflection points

 Identify characteristics of a function based on a graph of the

function or of its derivative

4.7 Find expressions for price, quantity, cost, revenue, and profit

 Find expressions for average cost, marginal cost, marginal

revenue, and marginal profit

 Minimize average cost

 Maximize profit

 Calculate and interpret elasticity of demand

 Maximize revenue at unit elasticity

 Minimize inventory costs