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Applied Calculus (MAT 121) Dr. Day Wednesday Feb 8, 2012

Applied Calculus (MAT 121) Dr. Day Wednesday Feb 8, 2012. Questions from Past Assignments? Applying Derivatives (Rate of Change) to Business and Economics (3.4) Assignments. Review: Limits and Derivatives. What do we mean when we say we are “ determining the limit of a function at a point ?”

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Applied Calculus (MAT 121) Dr. Day Wednesday Feb 8, 2012

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  1. Applied Calculus (MAT 121)Dr. Day Wednesday Feb 8, 2012 • Questions from Past Assignments? • Applying Derivatives (Rate of Change) to Business and Economics (3.4) • Assignments MAT 121

  2. Review: Limits and Derivatives • What do we mean when we say we are “determining the limit of a function at a point?” • Show a graphical and a numerical example to illustrate this. • Write a sentence or two to tie it all together. • What is our purpose in determining the derivative of a function? Why bother? • State the formal definition for the derivative of a function f(x). MAT 121

  3. Applications of Derivatives MAT 121

  4. Derivatives of Composite Functions (2.2,3.3) MAT 121

  5. Derivatives of Composite Functions (2.2,3.3) MAT 121

  6. Derivatives of Composite Functions (3.3) MAT 121

  7. MAT 121

  8. THE CHAIN RULE WORDS BY: JOHN A. CARTER TUNE: "CLEMENTINE" Here's a function in a function And your job here is to find The derivative of the whole thing With respect to x inside. Call the outside f of u And call the inside u of x. Differentiate to find df/du And multiply by du/dx. Use the chain rule. Use the chain rule. Use the chain rule whene'er you find The derivative of a function compositionally defined. MAT 121

  9. Using Rates of Change in Business and Economics 3.4) • For the Acrosonic model F loudspeaker system, the relationship between its unit price p, in dollars, and the quantity demanded x, is modeled by the function p = −0.02x +400, for 0 ≤ x ≤ 20,000. • Create the revenue function R for the model F system. • Calculate the marginal revenue function R’. • Compute R’(2000) and interpret that result within the context of the problem. • Suppose we also know that the cost function, to produce x units of the model F system, is C(x) = 100x + 200,000. • Create the profit function P(x). • Determine the marginal profit function P’. • Calculate P’(2000) and interpret that result. • Look at a graph of the profit function P and describe what is shows within the context of this problem. MAT 121

  10. Assignments WebAssign 2.2 and 3.3 tonight 3.4 due Friday night MAT 121

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