Functions and mappings

Differentiation rules

Marginal rate of substitution

Second derivative

Factorization

Running head: DECISION-MAKING IN AGRIBUSINESS 1 DECISION-MAKING IN AGRIBUSINESS 8 Decision-Making in Agribusiness: Quantitative Applications (AGSC5300) Name Institution Decision-Making in Agribusiness: Quantitative Applications (AGSC5300) Problem 1 To differentiate the function, Y=?lnX?, the chain rule is applied. Fundamentally, the rule states that, for a function of the form Y=f(f(X)) the derivative is computed as follows: First, let f(X) be a value, say U. The function may therefore be written as Y=f(U) Then, the function is differentiated with respect to U That is, Next, the derivative of U with respect to X is calculated That is, Combining the above two derivatives gives the chain rule: =* Applying the above rule, let X? be U Therefore, Y=?lnU.

bccalcclassact5aparametric

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Curves

Analytic geometry

equations

Multivariable calculus

Name:________________________ Date:________________________ AP Calculus BC Class Activity 5a: Parametric Equations Complete the value of table below and graph the curve for and y = t x y -2 -1 0 1 2 3 Complete the table below and graph the curve for and . t x y 0 ? 2? For the following problems eliminate the parameter and find y as a function of x. and and Given the function below and an equation for x, find one parametric curve that could represent it: and and Use

bccalcclassact4aconcavity

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Differential calculus

Convex analysis

Curves

Name:________________________ Date:________________________ AP Calculus BC Class Activity 4a: Concavity For the function , find and show where it is concave up on [0, 2?]. Find and show the points of inflection for the function . Find and show the points of inflection for the function . Given the function : Find the critical points for p (x), i.e. the candidates for local maximums and minimums. Use the second derivative test to show which points are maximums and which are minimums. Given the following graph for : Notate the intervals where f (x) is concave up. Notate the intervals where f (x) is concave down. Notate the points of inflection. Given the following graph for : Notate theintervals where g (x) is concave up.

bccalcclassact3bextremapt2mvt

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Name:________________________ Date:________________________ AP Calculus BC Class Activity 3b: Extrema Part 2 A point moves along the line so that its position can be found by the function Find the velocity and speed functions. Find and verify where the particle changes direction. At what position is the point furthest to the left? For what interval(s) is the point moving to the left? Given the graph below for , sketch a possible graph for : Given the graph below for , sketch a possible graph for : Given the graph below for , sketch a possible graph for : Given the following graph for : Find the local maximums and local minimums for . Find where the function is increasing and decreasing.

bccalcclassact1alimitslhopitals

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Interpersonal relationships

Human development

Name:________________________ Date:________________________ AP Calculus BC Class Activity 1a: Limits and L?Hopital?s Rule Evaluate the following limits: Use L'Hopital's Rule to evaluate the following:
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AP calc pre req practice test

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Analytic geometry

Asymptote

Limit of a function

AP Calculus AB Name:________________________________________ AP Problem Set: Prerequisites and Limits Signature (indicating you worked alone):___________________________________________ No calculator allowed. ALL WORK MUST BE COMPLETED ON A SEPARATE SHEET OF PAPER IN NUMERICAL ORDER WITH THIS SHEET STAPLED BEHIND IT. If I can?t read it, you will earn a 0 on this assignment. If your work does not support your answer choice, you will earn a 0 on this assignment! 1. If , then the inverse function, , is given by (A) (B) (C) (D) (E) 2. Which of the following function are continuous for all real numbers x? I. II. III. (A) None (B) I only (C) II only (D) I and II (E) I and III

ap calculus

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Differential calculus

rates

derivative

integral

Differentiation rules

Rahn ? 2008 AP Calculus ? Final Review Sheet When you see the words ?. This is what you think of doing 1. Find the zeros of a function. Set the function equal to zero and solve for x. 2. Find equation of the line tangent to f(x) at (a,f(a)). Find f ?(x),the derivative of f(x). Evaluate f ?(a). Use the point and the slope to write the equation: y= f ?(a)(x-a)+f(a) 3. Find equation of the line normal to f(x) at (a,f(a)). Find f ?(x),the derivative of f(x). Evaluate f ?(a). The slope of the normal line is 1 '( )f a ? . Use the point and the slope to write the equation: ( ) ( ) ( ) 1 y x a f a f ? a = ? + 4. Show that f(x) is even. Evaluate f at x = -a and x = a and show they are equal.

2008 AP mc

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Mathematics

Integral calculus

The questions contained in this AP? Calculus BC Practice Exam are written to the content specifications of AP Exams for this subject. Taking this practice exam should provide students with an idea of their general areas of strengths and weaknesses in preparing for the actual AP Exam. Because this AP Calculus BC Practice Exam has never been administered as an operational AP Exam, statistical data are not available for calculating potential raw scores or conversions into AP grades. This AP Calculus BC Practice Exam is provided by the College Board for AP Exam preparation. Teachers are permitted to download the materials and make copies to use with their students in a classroom setting

2008 AP MC

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