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Jeopardy Directions for the game: 1. You will need a pencil and paper to keep score.PowerPoint Presentation

Jeopardy Directions for the game: 1. You will need a pencil and paper to keep score.

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Directions for the game:

1. You will need a pencil and paper to keep score.

2. On the next screen, click ONCE on a question.

3. Read the Question and decide on your answer.

4. Click ONCE on the screen If you’re right, add your

points to your total. If you are wrong, subtract those

points.

5. Click ONCE on the button to go back to try

another question.

6. Ready? Click ONCE to go the the Jeopardy board!

7. Press the “Esc” button on the keyboard to end the game.

Have fun!

Home

Applications

Other stuff

Limits

Integrals

Misc.

Final Jeopardy

$100

$100

$100

$100

$100

$100

$200

$200

$200

$200

$200

$200

Scores

$300

$300

$300

$300

$300

$300

$400

$400

$400

$400

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$500

$500

$500

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Double

2X

(X+ΔX)^2 + 1 – X^1 -1

Δ X cancel 1’s

X^2 + 2XΔX + ΔX^2 – X^2

Δ X square and simplify

2X + Δ X

Δ X = 0

Answer = 2X.

Home

In an application problem relevant to motion, the first derivative of an equation tells ____________.

In an application problem relevant to motion, the second derivative tells ______________.

A hot-air balloon is rising straight up from a level field and is being tracked by a range finder located 500ft from the balloon. At the moment the range finder’s angle of elevation is π/4, the angle is increasing at the rate of 0.14 rad/min. How fast is the balloon rising at that moment?

Draw a picture

Θ = the angle the range finder makes with the ground

Y = the height of the balloon (in feet)

T = time, and θ and y are differentiable functions of t.

Y = 500 tan θ

Y’ = 500 (sec2θ)dθ/dt

Y’ = 500(2)(.14) = 140ft/min

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Air is being pumped into a spherical balloon to cause its volume to increase at a rate of 100cm3/s. How fast is the radius of the balloon increasing when the diameter is 50 cm?

Car A is traveling west at 50 mi/h while car B is traveling north at 60 mi/h. Both cars are headed towards intersection C. At what rate are the cars approaching each other when car A is 0.3 mi from the intersection, and car B is 0.4 mi from the intersection?

A farmer has 2400 feet of fencing to create a rectangular pen for his lamas next to their new barn. If the barn side off the pen does not need a fence, what are the dimensions of the pen with the largest area?

A = LW = xy

A = 2x + y = 2400

y = 2400 - 2x

A = x(2400 – 2x) = 2400x – 2x2

A’ = 2400 – 4x

X = 600 ft

Y = 1200 ft

Home

When is it good to use implicit differentiation?

In words, state the product rule and the quotient rule.

Product rule: first time the derivative of the second + second time the derivative of the first.

Quotient rule: bottom time the derivative of the top – top times the derivative of the bottom all divided by the bottom squared.

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y = 2π4

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