Derivatives Jeopardy Rates of Change Q $100 Q $100 Q $100 Q $100 Tangent Lines Basic Rules Products & Quotients Chain Rule (or not) Rates of Change Q $100 Q $100 Q $100 Q $100 Q $100 Q $200 Q $200 Q $200 Q $200 Q $200 Q $300 Q $300 Q $300 Q $300 Q $300 Q $400 Q $400 Q $400 Q $400 Q $400 Q $500 Q $500 Q $500 Q $500 Q $500 Final Jeopardy

$100 Question from H1 Write the equation of the line tangent to the graph of f(x) = 3x2 – 5 that passes through the point (2, 7).

$100 Answer from H1 y = 12x – 17

$200 Question from H1 Write the equation of the line tangent to the graph of f(x) = 4x3 + 3x2 – 2x that passes through the point (-1, 1).

$200 Answer from H1 y = 4x + 5

$300 Question from H1 Write the equation of the line tangent to the graph of f(x) = that passes through the point (4, 2).

$300 Answer from H1

$400 Question from H1 Name the coordinates of the point where the line tangent to the graph of f(x) = 3x2 – 5 is horizontal.

$400 Answer from H1 (0, -5)

$500 Question from H1 Name the coordinates of the points where the line tangent to the graph of f(x) = x3 – 48x is horizontal.

$500 Answer from H1 (-4, 128) and (4, -128)

$100 Question from H2 Find the derivative of the function below.

$100 Answer from H2

$200 Question from H2 Find the derivative of the function below.

$200 Answer from H2

$300 Question from H2 Find the derivative of the function below.

$300 Answer from H2

$400 Question from H2 Find the derivative of the function below.

$400 Answer from H2

$500 Question from H2 Find the derivative of the function below.

$500 Answer from H2

$100 Question from H3 Find the derivative of the function below.

$100 Answer from H3

$200 Question from H3 Find the derivative of the function below.

$200 Answer from H3

$300 Question from H3 Find the derivative of the function below.

$300 Answer from H3

$400 Question from H3 Find the derivative of the function below.

$400 Answer from H3

$500 Question from H3 Find the derivative of the function below.

$500 Answer from H3

$100 Question from H4 Find the derivative of the function below.

$100 Answer from H4

$200 Question from H4 Find the derivative of the function below.

$200 Answer from H4

$300 Question from H4 Find the derivative of the function below.

$300 Answer from H4

$400 Question from H4 Find the derivative of the function below.

$400 Answer from H4

$500 Question from H4 Find the derivative of the function below.

$500 Answer from H4

$100 Question from H5 The position for an object is given by s(t) = 2t2 - 6t - 4 , measured in feet with time in seconds. Find average velocity of the object on [1, 4].

$100 Answer from H5

$200 Question from H5 The position for an object is given by s(t) = 2t2 - 6t - 4 , measured in feet with time in seconds. Find the instantaneous velocity when t = 4.

$200 Answer from H5

$300 Question from H5 A city is hit by an Asian flu epidemic. Officials estimate that t days after the beginning of the epidemic, the number of persons sick with the flu is given by p(t) = 120t2 – 2t3, when 0 ≤ t ≤ 40. At what rate is the flu spreading ten days after the beginning of the flu epidemic?

$300 Answer from H5

$400 Question from H5 A ball rolls down a long inclined plane so that its distance s from its starting point after t seconds is s = 4.5t2 + 2t feet. When will its instantaneous velocity be 38 feet per second?

$400 Answer from H5

$500 Question from H5 A ball is dropped vertically from a height of 100 meters. Assume that the acceleration due to gravity has a magnitude of 10 m/s 2 . What is the velocity at t = 2 ?

$500 Answer from H5

Final Jeopardy Suppose that the amount of water in a holding tank at t minutes is given by V(t) = 2t2 – 16t + 35. Determine each of the following: Is the volume of the water increasing or decreasing at t = 1 minute? Is the volume of the water increasing or decreasing at t = 5 minutes? Is the volume of the water in the tank changing faster at t = 1 or at t = 5? Is the volume of the water in the tank not ever changing. If so, when?

Final Jeopardy Answer