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Math 191 Study Guide for Hour Quiz #3 on Chapter 4 C.S.Davis |
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You are responsible for the subject matter in chapter 4. The following topics are central in their importance. I have assigned a minimal number of exercises at the end of each topic from Calculus, by James Stewart, 6th ed. . Work more similar exercises if you need to do so in order to master the topics. |
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4.1 |
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1. |
Given a graph of a function, locate absolute extrema (absolute maximum and absolute minimum), and local extrema (local maximum and local minimum) values and where they occur. P211#3,5 |
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2. |
State the Extreme Value Theorem (EVT) |
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3. |
Find the critical numbers for a given function. P212#31,39 |
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4. |
Find absolute extrema using the closed interval method (which uses Fermat’s Theorem). P212#49,59 |
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4.2 |
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1. |
State the Mean Value Theorem (MVT) |
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2. |
Illustrate the MVT graphically by checking the hypothesis and estimating the values of c that satisfy the conclusion. P219#7,9 |
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3. |
Illustrate the MVT algebraically by checking the hypothesis and locating the value of c that satisfy the conclusion. P219#11,13 |
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4.3 |
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1. |
Graph functions (primarily polynomials) using calculus (without graphing calculator). |
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a. |
Find all critical numbers (both type I and type II). |
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b. |
Find intervals where the curve rises and falls (increasing and decreasing) (apply First Derivative Test). |
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c. |
Find all hypercritical values (both type I and type II). |
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d. |
Find intervals where the curve smiles and frowns (concave up and concave down). (apply Second Derivative Test) |
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e. |
Find all relative extrema using the information above. |
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f. |
Find all inflection points. |
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g. |
Draw a graph of the function which includes all of the information gathered above. P228#23,29,35 |
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2. |
Graph a functions given some information about the values of f, f ' and f ''. P228#21,25,27 |
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4.4 |
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1. |
Evaluate infinite limits and limits at infinity numerically, graphically and algebraically. P240#3,11,14,15,17,21,23,25 |
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2. |
Find Horizontal and Vertical Asymptote. P24137 |
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3. |
Find Horizontal Asymptote and use them along with concavity to sketch a curve. P241#45 |
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4. |
Sketch the graph of a function given facts about f, f', f''. "Connect the dots, dashes and bends." P242#51,53 |
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4.5 |
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1. |
Graph rational functions and more involved functions using Stewart’s eight guidelines: |
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a. |
domain |
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b. |
intercepts |
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c. |
symmetry |
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d. |
discontinuities, horizontal, vertical and slant asymptotes |
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e. |
intervals of rising and falling |
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f. |
critical numbers, extrema (absolute and local max/min values), (1st and 2nd Derivative Tests) |
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g. |
concavity and points of inflection (Concavity Tests) |
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h. |
sketch the curve |
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P248#11,13 |
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4.6 |
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1. |
Graph a function (using a graphing calculator) that reveals all important aspects of the curve. Locate and identify each one. P255#7,9,11 |
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4.7 |
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1. |
Solve optimization problems (max/min word problems) having interval domains to find absolute maxima or minima of: |
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a. |
areas of rectangles and triangles; P263#9,31 |
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b. |
volumes of rectangular solids, cylinders, cones; P264#13,27,29 |
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c. |
cost. P264#35 |
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d. |
(challange) P267#70 |
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4.8 |
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1. |
Use Newton's method--also called the Newton Raphson method–to find the root(s) of an equation numerically with great accuracy. P272#13,21 |
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