AD CALCULUS REVIEW JEOPARDY QUESTIONS DAVID LIU, SOPHIA PRATTO, AND CALEB BLANCHARD

JEOPARDY QUESTIONS ??? ? Chapter 2 Chapter 3 Chapter 5Mash-Up Final Jeopardy

SECTION 2-1 Problem: Find an equation of the tangent line to f(x)=x 2 +2x+6 at the point (2,14) xf(x) xf(x) Solution:

SECTION 2-2 Problem: State the value of each quantity if it exists: Solution: a)1.5 b)9 c)DNE d)3

SECTION 2-3 CALCULATING LIMITS USING LIMIT LAWS Problem: Find the values of the following limits. Solution: A) 5 B) 4 C) 2 D) 5

SECTION 2-3 THE SQUEEZE THEOREM Problem: Solve the following limit. Solution: 350 Points!

SECTION 2-4 Problem: Solution:

SECTION 2-5 Problem: Is f(x) continuous at x = 3? Solution:

SECTION 2-6 Problem: Solution:

SECTION 2-7

SECTION 2-8 Problem: Solution:

SECTION 3-1 Problem: Differentiate 4x x 2 + 7x - 2e x + 6 Solution: 12x x e x

SECTION 3-2 Problem: Find the derivative of: Solution:

SECTION 3-3 Problem: Find f’’(x) when f(x) = 3sin(x) – 2cos(x) Solution: f’(x) = 3cos(x) + 2sin(x) f’’(x) = -3sin(x) + 2cos(x)

SECTION 3-4 Problem: Find the derivative of Solution:

SECTION 3-5 IMPLICIT DIFFERENTIATION y – 1 = -2(x-1) or y = -2x +3

SECTION 3-5 INVERSE TRIG FUNCTIONS 300 points!

SECTION 3-6 DERIVATIVES OF LOG FUNCTIONS Problem Find f’(x) if Solution:

SECTION 3-6 LOGARITHMIC DIFFERENTIATION

SECTION 3-8 EXPONENTIAL GROWTH Problem: If a bacteria culture that grows with constant relative growth rate initially contains 300 cells, and after an hour, contains 2,080 cells, find the number of bacteria after 4 hours. Solution: 600 points! y ≈ 691,917 bacteria

SECTION 3-8 NEWTON’S LAW OF COOLING Problem: A cup of hot cocoa is 90°C at room temperature (20°C). After sitting outside (0°C) for 20 mins, it cools to 40 degrees. What is the temperature of the cocoa after another 10 minutes outside? Solution: T = 26.6°C

SECTION 3-9 Problem: An inverted conical tank with a 5 foot radius is being filled with water at a rate of 11 cubic meters per minute. How fast is the height of the water increasing? Solution:

SECTION 3-10 = 6.042

SECTION 5-1 Problem: Use four left-hand rectangles to approximate the area under the curve Solution:

SECTION 5-1 Problem: Use four midpoint rectangles to approximate the area under the curve Solution:

SECTION 5-1 Problem: Use infinitely many rectangles to evaluate the area of the region bounded by f(x) = 3x + 2, x = 0, and x = 2 Solution:

SECTION points!

SECTION 5-3

SECTION 5-4

FINAL JEOPARDY! Solution

FINAL JEOPARDY SOLUTION Increasing: Decreasing: Local Max Value: 81 Local Min Value: 0 Concave Up: Concave Down: Points of Inflection: