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Chapter 4: Applications of Differentiation

Expert-verified
Essential Calculus: Early Transcendentals
Pages: 203 - 256
Essential Calculus: Early Transcendentals

Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280

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Illustration

368 Questions for Chapter 4: Applications of Differentiation

  1. Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.

    Found on Page 254

  2. Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have.

    Found on Page 238

  3. Find the most general antiderivative of the function. (Check your answer by differentiation.)

    Found on Page 252

  4. (a) Find the vertical and horizontal asymptotes, if any

    Found on Page 255

  5. (a) Determine the intervals on which the function \(f(x) = {x^4}{e^{ - x}}\) is increasing or decreasing.

    Found on Page 222

  6. Sketch the graph of a function that is continuous on (1, 5) and has the given properties.

    Found on Page 208

  7. 9–12 ■ Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval. Then find all numbers that satisfy the conclusion of the Mean Value Theorem.

    Found on Page 215

  8. Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have.

    Found on Page 238

  9. (a) Sketch the graph of a function that satisfies the conditions that the graph has local maximum at 2 and is differentiable at 2.

    Found on Page 208

  10. 9–12 ■ Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval. Then find all numbers that satisfy the conclusion of the Mean Value Theorem.

    Found on Page 215

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