Derivatives Jeopardy Tangent Lines Basic Rules Products Quotients
Derivatives Jeopardy Tangent Lines Basic Rules Products & Quotients Chain Rule (or not) Rates of Change Q $100 Q $100 Q $200 Q $200 Q $300 Q $300 Q $400 Q $400 Q $500 Q $500 Final Jeopardy
$100 Question from H 1 Write the equation of the line tangent to the graph of f(x) = 3 x 2 – 5 that passes through the point (2, 7).
$100 Answer from H 1 y = 12 x – 17
$200 Question from H 1 Write the equation of the line tangent to the graph of f(x) = 4 x 3 + 3 x 2 – 2 x that passes through the point (-1, 1).
$200 Answer from H 1 y = 4 x + 5
$300 Question from H 1 Write the equation of the line tangent to the graph of f(x) = that passes through the point (4, 2).
$300 Answer from H 1
$400 Question from H 1 Name the coordinates of the point where the line tangent to the graph of f(x) = 3 x 2 – 5 is horizontal.
$400 Answer from H 1 (0, -5)
$500 Question from H 1 Name the coordinates of the points where the line tangent to the graph of f(x) = x 3 – 48 x is horizontal.
$500 Answer from H 1 (-4, 128) and (4, -128)
$100 Question from H 2 Find the derivative of the function below.
$100 Answer from H 2
$200 Question from H 2 Find the derivative of the function below.
$200 Answer from H 2
$300 Question from H 2 Find the derivative of the function below.
$300 Answer from H 2
$400 Question from H 2 Find the derivative of the function below.
$400 Answer from H 2
$500 Question from H 2 Find the derivative of the function below.
$500 Answer from H 2
$100 Question from H 3 Find the derivative of the function below.
$100 Answer from H 3
$200 Question from H 3 Find the derivative of the function below.
$200 Answer from H 3
$300 Question from H 3 Find the derivative of the function below.
$300 Answer from H 3
$400 Question from H 3 Find the derivative of the function below.
$400 Answer from H 3
$500 Question from H 3 Find the derivative of the function below.
$500 Answer from H 3
$100 Question from H 4 Find the derivative of the function below.
$100 Answer from H 4
$200 Question from H 4 Find the derivative of the function below.
$200 Answer from H 4
$300 Question from H 4 Find the derivative of the function below.
$300 Answer from H 4
$400 Question from H 4 Find the derivative of the function below.
$400 Answer from H 4
$500 Question from H 4 Find the derivative of the function below.
$500 Answer from H 4
$100 Question from H 5 The position for an object is given by s(t) = 2 t 2 - 6 t - 4 , measured in feet with time in seconds. Find average velocity of the object on [1, 4].
$100 Answer from H 5
$200 Question from H 5 The position for an object is given by s(t) = 2 t 2 - 6 t - 4 , measured in feet with time in seconds. Find the instantaneous velocity when t = 4.
$200 Answer from H 5
$300 Question from H 5 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) = 120 t 2 – 2 t 3, when 0 ≤ t ≤ 40. At what rate is the flu spreading ten days after the beginning of the flu epidemic?
$300 Answer from H 5
$400 Question from H 5 A ball rolls down a long inclined plane so that its distance s from its starting point after t seconds is s = 4. 5 t 2 + 2 t feet. When will its instantaneous velocity be 38 feet per second?
$400 Answer from H 5
$500 Question from H 5 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 H 5
Final Jeopardy Suppose that the amount of water in a holding tank at t minutes is given by V(t) = 2 t 2 – 16 t + 35. Determine each of the following: a) Is the volume of the water increasing or decreasing at t = 1 minute? b) Is the volume of the water increasing or decreasing at t = 5 minutes? c) Is the volume of the water in the tank changing faster at t = 1 or at t = 5? d) Is the volume of the water in the tank not ever changing. If so, when?
Final Jeopardy Answer
- Slides: 53