Chapter 3: Differentiation Section 3.1: Definition of the Derivative

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Chapter 3: Differentiation Section 3.1: Definition of the Derivative Jon Rogawski Calculus, ET First Edition Chapter 3: Differentiation Section 3.1: Definition of the Derivative Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

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

How might we use the slope of the secant line in Figure 1(A) and limits to find the slope of the tangent line in Figure 1(B)? Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Figure 2 illustrates how the slope of the secant line PQ approaches the slope of the tangent line as Q approaches P. 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

Example, Page 124 Compute f ′(a) in two ways, using Equations (1) and (2). 3. f (x) = x2 + 9x, a = 0 Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 124 Compute f ′(a) in two ways, using Equations (1) and (2). 3. f (x) = x2 + 9x, a = 0 Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

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

Find the equation of the tangent line to y = x2 at x = 5. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Find the equation of the tangent line to y = x–1 at x = 2. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

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