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Chapter 4 and 5 Jeopardy

Chapter 4 and 5 Jeopardy. Insight Questions. Finding the Derivative. Applications of Derivatives. Chapter 5. 100. 100. 100. 100. 200. 200. 200. 200. 300. 300. 300. 300. 400. 400. 400. 400. 500. 500. 500. 500. Final Jeopardy.

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Chapter 4 and 5 Jeopardy

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  1. Chapter 4 and 5 Jeopardy Insight Questions Finding the Derivative Applications of Derivatives Chapter 5 100 100 100 100 200 200 200 200 300 300 300 300 400 400 400 400 500 500 500 500 Final Jeopardy

  2. If f’(x) = g’(x), then what can you say about f(x) and g(x)? A-100

  3. Sketch a graph who has the following properties: Explain your graph A-200

  4. A-300

  5. Sketch the function: Then sketch and explain f’(x). A-400

  6. State and explain the formal definition of a derivative. Use a graph in your explanation. A-500

  7. Find the derivative: B-100

  8. B-200 Find the derivative of the function:

  9. B-300 Find the derivative of the function by using the definition of the derivative:

  10. Find the derivative of the function: B-400

  11. B-500 Use implicit differentiation to find the derivative:

  12. C-100 The edges of a cube are expanding at a rate of 3 cm per second. Find the rate of change of the volume of a cube with sides of 4 cm

  13. C-200 Find the rate of change of the distance between the origin and a moving point on the graph of

  14. C-300 The radius of a right circular cylinder is given by Where t is time in seconds and dimensions are in inches. Find the rate of change of the volume with respect to time.

  15. C-400 A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius of the outer ripple is increasing at a constant rate of 2 foot per second. When the radius is 4 feet, at what rate is the total area of the disturbed water changing?

  16. C-500 A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. Water is flowing into the tank at a rate of 10 cubic feet per minute. Find the rate of change of the depth of the water when the water is 8 feet deep.

  17. D-100 If Rolle’s Theorem can be applied, find all values of c in the open interval (a, b) such that f’(c)=0

  18. D-200

  19. D-300 Find the point(s) guaranteed by the Mean Value Theorem for the closed interval [a, b]

  20. D-400 • Find the critical numbers of f • find the open intervals on which the function is increasing or decreasing • Apply the First Derivative Test to identify all relative extrema

  21. D-500 • Find the critical numbers of f • find the open intervals on which the function is increasing or decreasing • Apply the First Derivative Test to identify all relative extrema

  22. FINAL JEOPARDY Use symmetry, extrema, and zeros to sketch the graph of f

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