Calculus I Recitation Session #7 (4.1 and 4.2)
Summary of important concepts
4.1
[1] Relative (local) maximum and relative (local) minimum (a) f (c) is a local maximum if it is the greatest for all x from a small neighborhood of c (top of hill) f (c) is
ADDITIONAL RELATED RATE PROBLEMS
1. A ladder 20 feet long leans against a vertical building. If the bottom of the ladder slides away from the building horizontally at a rate of 2 ft/sec, how fast is the ladder sliding down the building when the top of the
Rolles Theorem Let f be a function that satisfies the following three hypotheses: 1) f is continuous on the closed interval [a , b] . 2) f is differentiable on the open interval ( a , b) .
3)
f ( a ) = f ( b)
Then there is a number c in ( a , b) such that
ROLLES THEOREM AND THE MEAN VALUE THEOREM
WILLIAM A. LAMPE
Recall the Theorem on Local Extrema. If f (c) is a local extremum, then either f is not dierentiable at c or f (c) = 0. That is, at a local max or min f either has no tangent, or f has a horizonta
practice test ch4
Multiple Choice Identify the choice that best completes the statement or answers the question. _ 1. Find all the critical numbers of the function: . a. b. c. d. _ 2. Find the critical numbers of the function: .
_
a. 9, 0 b. 81, -81 c. 9,
Calculus (MAT 220) - Extreme Values and MVT (Solutions) Extreme values 1. Sketch the graph of a function that satisfies each of the following (five different functions): (a) f attains both a maximum and a minimum on [0, 5] and is continuous on [0, 5].
35
4.7 Exercises for Optimization Problems 1. Find the greatest possible value of xy given that x and y are both positive and x + y = 40.
A) B) C) D)
200 160 400 320 Ans: (C)
2. What is the smallest perimeter possible for a rectangle whose area is to be 28 s