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Derivatives Tangent Lines & Rates of Change Applications of derivatives Integration Applications of Integration Pot Pourri

NO Calculator A 100

-2 A 100 Correct Response One A

A 200 NO Calculator

± 2 A 200

A 300

E

A 400

A

A 500

An equation of the line tangent to the graph of y = cos 3x at x = π/6 B 100 NO Calculator

B 100

At what point on the graph of y = ½ x – 3/2 is the tangent line parallel to the line 4x – 8y = 5 ? B 200 NO Calculator THERE IS A MISTAKE ON THIS SLIDE…SKIP IT

B 200

Let f be differentiable such that f(5) = 3 and f’(5)=2. If the tangent line to the graph of f at x = 5 is used to find an approximation to a zero of f, that approximation is B 300 NO Calculator

3.5 B 300

Calculator Active B 400 Let f be the function given by For what positive value of a is the slope of the line tangent to the graph of f at (a, f(a)) equal to 6?

0.344 B 400

B 500 NO Calculator

1/16 B 500

is concave down for what values of x? C 100 NO Calculator

C 100

Calculator Active C 200 (A) (B) 0.259(C) (D) 2.543(E) 3.310

C C 200

Calculator Active C 300 The graph of the function changes concavtiy at x = ?

2.207 C 300

DAILY DOUBLE C 400 DAILY DOUBLE Place A Wager

Two roads cross at right angles, one running north/south and the other east/west. Eighty feet south of the intersection is an old radio tower. A car traveling at 50 feet per second passes through the intersection heading east. At how many feet per second is the car moving away from the radio tower 3 seconds after it passes through the intersection? C 400 Calculator Active

44.12 C 400

Let f be a function such that f”(x) < 0 for all x in the closed interval [3,4], with selected values shown in the table. Which of the following must be true? C 500 X F(x) (A) f’(3.3) < 0(B) 0 < f’(3.3) < 1.6 (C)1.6 < f’(3.3) < 1.8(D) 1.8 < f’(3.3) < 2.0 (E) f’(3.3) > 2.0

D C 500

D 100 NO Calculator

D

D 200

e t/3 + C D 200

D 300

8b – 3a D 300

D 400

D 500 NO Calculator

D – e

The area of the region enclosed by the graph of y = x and the line y = 11 E 100 NO Calculator

36 E 100

No Calculator E 200 If the region enclosed by the y-axis, the line y = 2, and the curve is revolved about the y-axis, the volume of the solid generated is

E 200

Calculator Active E 300

0.941 E 300

Calculator Active E 400 At time t > 0, the acceleration of a particle that is moving along the x-axis is a(t) = t + 2sin(t). At t = 0, the velocity of the particle is -4. For what value of t will the velocity of the particle be zero?

1.78 E 400

E 500 Calculator Active Round to 5 decimal places The average value of f(x) = -sinx on the interval [-2, 4] is

E 500

F 100 NO Calculator

5 F 100

If y = 3x + 6, what is the minimum value of x 3 y? F 200 Calculator Active

F 200

NO Calculator F 300

-25/64 F 300

No Calculator F 400

B

F 500

2.507

The Final Jeopardy Category is: Differential Equation Please record your wager. Click on screen to begin

A crate of supplies is dropped from an airplane with a remote-controlled parachute. Let v(t) be the velocity (in m/s) of the crate at time t seconds, t > 0. After the parachute opens, the velocity of the crate satisfies the differential equation dv/dt = -3v – 15, with initial condition v(0) = -15. a)Find an expression for v in terms of t. b)Find the terminal velocity of the crate. (terminal velocity is Click on screen to continue

a) b) -5 m/sec Click on screen to continue

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