Homework Homework Assignment #16 Read Section 3.8 Page 178, Exercises: 1 – 93 (EOO) Quiz next time Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 Fill in the table. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 Write the function as a composition and find the derivative. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 Find the derivative. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 Find the derivative. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 Find the derivative of f ○ g. 17. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 Find the derivative. 21. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 Find the derivative. 25. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 Find the derivative. 29. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 Find the derivative. 33. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 Find the derivative. 37. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 Find the derivative. 41. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 Find the derivative. 45. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 Find the derivative. 49. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 Find the derivative. 53. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 Find the derivative. 57. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 Find the derivative. 61. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 Find the derivative. 65. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 Find the derivative. 69. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 73. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 77. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 Use the table of values to calculate the derivative of the function at the given point. 81. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 Compute the indicated higher derivatives. 85. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 89. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 93. The force F (Newtons) between two charged particles is F = 100/r2, where r is the distance (meters) between them. Find dF/dt at t = 10 if distance at time t (sec) is r = 1 + 0.4t2. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Chapter 3: Differentiation Section 3.8: Implicit Differentiation Jon Rogawski Calculus, ET First Edition Chapter 3: Differentiation Section 3.8: Implicit Differentiation Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

The graph in Figure 1 is not that of a function, but of a relation. It is said that y is defined implicitly, as it could be difficult or impossible to solve the equation for y. To find the slope of the tangent line, we must use implicit differentiation. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

in question? Consider the equation for the unit circle x2 + y2 = 1. Consider the unit circle shown in Figure 2. How do we determine the slope at the point in question? Consider the equation for the unit circle x2 + y2 = 1. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

The relation y4 + xy = x3 – x + 2 may be broken down into two functions, each defining a branch of the curve and neither violating the vertical line rule. The point where the branches split is the point at which the curve has a vertical slope. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Find the equation of the tangent to the curve y4 + xy = x3 – x + 2 Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework Homework Assignment #17 Read Section 3.9 Page 184, Exercises: 1 – 49 (EOO) Rogawski Calculus Copyright © 2008 W. H. Freeman and Company