1. Homework, Page 139 Compute f ′ (x) using the limit definition.
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2. Homework, Page 139 Compute f ′ (x) using the limit definition.
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3. Homework, Page 139 Use the Power Rule to compute the derivative.
Rogawski Calculus
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4. Homework, Page 139 Use the Power Rule to compute the derivative.
Rogawski Calculus
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5. Homework, Page 139
Compute f ′ (a) and find an equation of the tangent line to the graph at x = a.
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6. Homework, Page 139 21. Calculate: Rogawski Calculus
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7. Homework, Page 139 Calculate the derivative of the function.
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8. Homework, Page 139 Calculate the derivative of the function.
Rogawski Calculus
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9. Homework, Page 139 Calculate the derivative of the function.
Rogawski Calculus
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10. Homework, Page 139 Calculate the derivative of the function.
Rogawski Calculus
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11. Homework, Page 139 Calculate the derivative indicated.
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12. Homework, Page 139 Calculate the derivative indicated.
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13. Homework, Page 139
49. Sketch the graph of f ′(x) for f (x) omitting points where f (x) is not differentiable.
Rogawski Calculus
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14. Homework, Page 139
53. Find the points on the curve y = x2 + 3x – 7 at which the slope of the tangent line is equal to 4..
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15. Homework, Page 139
57. Determine the coefficients a and b such that p(x) = x2 + ax + b satisfies p(1) = 0 and p′(1) =4.
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16. Homework, Page 139
61. Compute the derivative of f (x) = x–2 using the limit definition.
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17. Homework, Page 139 65. Rogawski Calculus
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18. Homework, Page 139
Let L be a tangent line to the hyperbola xy = 1 at x = a, where a > 0. Show that the area of the triangle bounded by L and the coordinate axes does not depend upon a.
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19. Homework, Page 139 71. Match the functions (A – C)
with their derivatives (I – III) in
Figure 18.
A – III
B – I
C – II
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20. Homework, Page 139
Make a rough sketch of the graph of the derivative of the function shown in Figure 19(A).
Rogawski Calculus
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21. Chapter 3: Differentiation Section 3.3: Product and Quotient Rules
Jon Rogawski Calculus, ET First Edition
Chapter 3: Differentiation
Section 3.3: Product and Quotient Rules
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22. As noted above, the derivative of a product is NOT the product
of the derivatives.
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23. Example, Page 148 Use the Product Rule to find the derivative.
Rogawski Calculus
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24. Example, Page 148 Use the Product Rule to find the derivative.
Rogawski Calculus
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25. Example, Page 148 Use the Product Rule to find the derivative.
Rogawski Calculus
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26. Example, Page 148 Use the Product Rule to find the derivative.
Rogawski Calculus
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27. As noted above, the derivative of a quotient is NOT the quotient
of the derivatives.
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28. Example, Page 148 Use the Quotient Rule to find the derivative.
Rogawski Calculus
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29. Example, Page 148 Use the Quotient Rule to find the derivative.
Rogawski Calculus
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30. Example, Page 148
Use the Quotient Rule to find the derivative, then evaluate.
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31. Example, Page 148
Use the Quotient Rule to find the derivative, then evaluate.
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32. The power P delivered to load R by the battery (V and
r are constants) is:
(a) Calculate dP/dR; (b) Find the value of R where the tangent to the
graph of P is horizontal.
Rogawski Calculus
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33. The power P delivered to load R by the battery (V and
r are constants) is:
(a) Calculate dP/dR; (b) Find the value of R where the tangent to the
graph of P is horizontal.
Rogawski Calculus
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34. Rogawski Calculus
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35. WS 3.3.pdf Rogawski Calculus
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