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Applied Calculus (MAT 121) Dr. Day Thursday Feb 2, 2012

Applied Calculus (MAT 121) Dr. Day Thursday Feb 2, 2012. Review Meaning and Definition of the Derivative (2.6) Shortcut Rules for Determining Derivatives (3.1 ) Applications Requiring Use of Derivatives (2.6, 3.1) Derivatives of Products and Quotients (3.2) Assignments & Test #1 Results.

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Applied Calculus (MAT 121) Dr. Day Thursday Feb 2, 2012

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  1. Applied Calculus (MAT 121)Dr. Day Thursday Feb 2, 2012 Review • Meaning and Definition of the Derivative (2.6) • Shortcut Rules for Determining Derivatives (3.1) • Applications Requiring Use of Derivatives (2.6, 3.1) • Derivatives of Products and Quotients (3.2) • Assignments & Test #1 Results 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. Applications of Derivatives MAT 121

  5. Review: Shortcuts for Determining Derivatives (3.1) MAT 121

  6. Shortcut Rules for Determining Derivatives (3.1) • What if the function is a constant function? y = k • What if the function is a power function? y = xn • What if the function includes a coefficient? y = cf(x) • What if the function is the sum or difference of several functions? y = cf(x) + dg(x) Applications of Derivatives MAT 121

  7. Shortcut Rules for Derivatives (3.1) • What if the function is a constant function? y = k • The derivative of any constant function is 0: If y = f(x) = k, then y’ = f’(x) = 0 MAT 121

  8. Shortcut Rules for Derivatives (3.1) • What if the function is a power function? y = xn If y = f(x) = xn, then y’ = f’(x) = nxn-1. MAT 121

  9. Shortcut Rules for Derivatives (3.1) • What if the function includes a coefficient? y=cf(x) If y = cf(x), then y’ = cf’(x). MAT 121

  10. Shortcut Rules for Derivatives (3.1) • What if the function is the sum or difference of several functions? y=cf(x) + dg(x) If y = cf(x) + dg(x), then y’ = cf’(x) + dg’(x). MAT 121

  11. Derivatives of Products (3.2) If y = h(x) = f(x)g(x), then y’ = h’(x) = f’(x)g(x) + f(x)g’(x) The derivative of a product of two functions is: The derivative of the first times the second plus the first times the derivative of the second. MAT 121

  12. Derivatives of Quotients (3.2) If: Then: The derivative of a quotient of two functions is: The derivative of the top times the bottom minus the top times the derivative of the bottom All over The bottom squared. MAT 121

  13. Assignments WebAssign • 3.1 tonight • 3.2 Friday night MAT 121

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