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Below are the objectives for CP Calculus.  Click on the link  for students or  for teachers for any objective to see the resources available or to add your own resource.

Home - Math – CP Calculus

 

Standard 4: Patterns, Functions and Algebra

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Benchmark

Indicator

 

A.  Analyze functions by investigating rates of change, intercepts,         zeros, asymptotes, and local and global behavior.

1.   Analyze the roots of the derivative to find the critical numbers             of f(x).

2.   Analyze f '(x) to find the slope of a curve and the equation of the tangent to the curve at a point.

3.   Analyze the zeros and values of f '(x) on intervals to find the        absolute and relative maximums and minimums of f(x).

4.   Analyze the values of f '(x) to find where f(x) is increasing or decreasing.

5.   Analyze the zeros and values of f ''(x) to find the points of      inflection and concavity of f(x).

6.   Analyze the first and second derivatives of the position             function to find the velocity and acceleration functions,   respectively.

7.   Evaluateto find the instantaneous rate of change of f(x)           at x = c.

8.   Evaluate antiderivatives to find distance and       velocity from           acceleration with initial conditions.

9.   Analyze the definite integral to find the average value of a         function on an interval.

10. Find solutions to growth and decay problems by       solving.

11. Evaluate functions whose limit at certain x-values is k.

 

C.  Apply methods to represent, generalize and solve problem    situations.

1.   Evaluate a limit in indeterminate form by rewriting the      function using algebraic manipulation to create an equivalent        function.

2.   Evaluate a limit at infinity by dividing every term by the       highest-powered term in the denominator.

3.   Identify and solve for the equation(s) of any       asymptotes of the    graph of a function.

4.   Solve optimization problems by analyzing the derivative.

5.   Apply the method of finding a derivative using implicit differentiation.

6.   Solve related rates problems using implicit differentiation.

7.   Apply the technique of integration by substitution (change of   variables) to find the integral.

 

D.  Apply formulas and theorems appropriately to problem            situations.

1.   Apply formulas developed via the Squeeze Theorem where             applicable to find limits.

2.   Apply the Intermediate Value Theorem to find a zero.

3.   Apply the Power Rule to find the derivative of a polynomial.

4.   Apply formulas for the derivatives of the six trigonometric     ratios.

5.   Apply the Product Rule to find the derivative of the product of            two or more functions.

6.   Apply the Quotient Rule to find the derivative of the quotient   of two functions.

7.   Apply the Chain Rule to find the derivative of composite         functions.

8.   Solve for the value at which the instantaneous rate of change   is the same as the average rate of change on an interval using        the Mean Value Theorem.

9.   Employ established rules and techniques to find the             derivatives of inverse functions (including logarithmic,    exponential, and trigonometric functions).

10.  Approximate the value of the definite integral using rectangles             (Riemann Sum) and trapezoids (Trapezoidal Rule).

11.  Evaluate a definite integral using the Fundamental Theorem   of Calculus.

12.  Evaluate the derivative using the Second Fundamental     Theorem of Calculus.

13.  Employ basic integration formulas to find the antiderivative.

 

E.   (8-10)  Analyze and compare functions and their graphs.

1.   Evaluate limits by inspecting the graph of the function.

2.   Evaluate limits at infinity as the value of a horizontal          asymptote.

3.   Demonstrate the understanding of the derivative as the slope    of a curve at a point.

4.   Describe the characteristics of a function based on the      analysis of its first and second derivatives.

5.   Sketch a precise graph of f(x) by inspecting the graphs of  f '(x)  and  f ''(x).

6.   Estimate the instantaneous rate of change of f(x) at a point on            the graph of f(x).

7.   Evaluate differential equations by looking at their Slope         Fields and vice versa.

 

F.   Demonstrate expertise with the graphing calculator.

1.   Visually compare the graphs of f(x), f '(x), and f ''(x) to            describe the impact of each upon the other.

2.   Find roots, intersection, extremes, slope at a       point, and area         under the curve for any function.

3.   Explore the direction, extremes, concavity, and inflection           points of a function.

 

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