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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
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

a 400
Sketch the function:

Then sketch and explain f’(x).

A-400
b 200
B-200

Find the derivative of the function:

b 300
B-300

Find the derivative of the function by using the definition of the derivative:

b 500
B-500

Use implicit differentiation to find the derivative:

c 100
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

c 200
C-200

Find the rate of change of the distance between the origin and a moving point on the graph of

c 300
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.

c 400
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?

c 500
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.

d 100
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

d 300
D-300

Find the point(s) guaranteed by the Mean Value Theorem for the closed interval [a, b]

d 400
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
d 500
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
final jeopardy
FINAL JEOPARDY

Use symmetry, extrema, and zeros to sketch the graph of f