Unit 7: Derivatives of Exponential and Logarithmic Functions 1 .8.1 Derivatives of Exponential Functions - define e 3. 8.3 Derivatives of General Exponential and - Be able to apply the derivative of Logarithmic Functions - Be able to apply the derivatives of 2. 8.2 The Derivative of the Natural Logarithmic Function - know the laws or logarithms and be able to 4. 8.4 Optimization Problems simplify functions using the laws. - the process of optimization with - define the natural logarithm exponential and logarithmic functions. - Be able to prove and apply the derivative of y = ln x Unit 8: Curve Sketching Review functions. Prerequisite Skills: - solving inequalities - division of polynomials 9.3 Vertical, Horizontal - define: infinite limits, one-sided infinite limits, finite Domain limits at infinity Determine the domains for of functions that will be - state conditions for rational functions to have vertical, analysed in this unit. Including rational and radical horizontal and linear oblique asymptotes expressions. - determine the vertical, horizontal, or oblique asymptote(s) of a rational function and the behaviour of 9.1 Increasing and Decreasing Functions the function close to the asymptote. - define when functions are increasing or decreasing on an interval. 9.3 Oblique Asymptotes - state conditions on the first derivative for functions to - outline a process to find oblique asymptotes and apply be increasing or decreasing - use conditions to determine where a function is increasing or decreasing. 9.4 Concavity and Points of Inflection - work through investigations on p. 363 - summarize conditions for concavity, the second 9.2 Critical Points, Relative Maxima, and Relative derivative test and points of inflection Minima - state conditions for: -absolute maximum or minimum values - relative maximum or minimum values 9.5 An Algorithm for Graph Sketching - critical numbers - outline steps for analysis and curve sketching - important numbers - examples of polynomial, rational, exponential and - use the conditions to determine relative maxima or logarithmic functions. minima, critical and important numbers for various
Unit 7: Derivatives of Exponential and Logarithmic Functions 1 .8.1 Derivatives of Exponential Functions - define e - Be able to apply the derivative of 2. 8.2 The Derivative of the Natural Logarithmic Function - know the laws or logarithms and be able to simplify functions using the laws. - define the natural logarithm - Be able to prove and apply the derivative of y = ln x 3. 8.3 Derivatives of General Exponential and Logarithmic Functions - Be able to apply the derivatives of 4. 8.4 Optimization Problems - the process of optimization with exponential and logarithmic functions. Unit 8: Curve Sketching Review Prerequisite Skills: - solving inequalities - division of polynomials Domain Determine the domains for of functions that will be analysed in this unit. Including rational and radical expressions. 9.1 Increasing and Decreasing Functions - define when functions are increasing or decreasing on an interval. - state conditions on the first derivative for functions to be increasing or decreasing - use conditions to determine where a function is increasing or decreasing. 9.2 Critical Points, Relative Maxima, and Relative Minima - state conditions for: -absolute maximum or minimum values - relative maximum or minimum values - critical numbers - important numbers - use the conditions to determine relative maxima or minima, critical and important numbers for various functions. 9.3 Vertical, Horizontal - define: infinite limits, one-sided infinite limits, finite limits at infinity - state conditions for rational functions to have vertical, horizontal and linear oblique asymptotes - determine the vertical, horizontal, or oblique asymptote(s) of a rational function and the behaviour of the function close to the asymptote. 9.3 Oblique Asymptotes - outline a process to find oblique asymptotes and apply 9.4 Concavity and Points of Inflection - work through investigations on p. 363 - summarize conditions for concavity, the second derivative test and points of inflection 9.5 An Algorithm for Graph Sketching - outline steps for analysis and curve sketching - examples of polynomial, rational, exponential and logarithmic functions.
Calculus%20Review%20Outline%20June%202015.docx