Curve sketching using calculus part 1 of 2 youtube. A candidate for a vertical asymptote is the place where the denominator goes to zero, which in this case is x 3. The following is a list of worksheets and other materials related to math 122b and 125 at the ua. A range of \t\s for a single trace of the parametric curve. Sketchingsurfacesin3d university of british columbia. In many applied problems we want to find the largest or smallest value that a function achieves for example, we might want to find the minimum cost at which. Find the domain of the function and determine the points of discontinuity if any. Calculus ii parametric equations and curves practice. A penguin is climbing up a long slippery slope, taking occasional breaks to slide back down for a bit. Level 4 challenges on brilliant, the largest community of math and science problem solvers. Curve sketching practice questions above handout 5. General rules more practice curve sketching is not my favorite subject in calculus, since its so abstract, but its useful to be able to look at functions and their characteristics by simply taking derivatives and thinking about the functions. The ten steps of curve sketching each require a specific tool. Increasing and decreasing functions first derivative.
Thus, before you to get to actual curve sketching, youll probably see some problems as in this section. Be sure to nd any horizontal and vertical asymptotes, show on a sign chart where the function is increasingdecreasing, concave upconcave down, and identifying as ordered pairs all relative extrema and in ection points. Find the length of the curve rt h12t,8t32,3t2i from t 0 to t 1. The following six pages contain 28 problems to practice curve sketching and extrema problems. Curve sketching warmup practice problems online brilliant. If your students need practice with the algebraic portion of the curve sketching process, see my cal. Using this information, we sketch the curve in figure 2. Selection file type icon file name description size revision time user. The chapter headings refer to calculus, sixth edition by hugheshallett et al.
It is also recommended that you complete the general curve sketching test on the ilrn website and the questions from the curve sketching sample problems page. Use derivatives to analyze properties of a function. Erdman portland state university version august 1, 20 c 2010 john m. To test your knowledge of curve sketching problems, try taking the general curve sketching test on the ilrn website or. Calculus iii practice questions 5 is the point on the curve y ex with maximum curvature. Find points with f00x 0 and mark sign of f00x on number line. Practice problem 3 modify your program from problem 2 to report, for any polynomial function, the intervals where. Problems for vertical and horizontal asymptotes 7 sparknotes. Mathematics learning centre, university of sydney 2 figure 1.
What does the graph of the following function look like. Determine the coordinates of all the stationary points of c and the nature of each. Each image is approximately 150 kb in size and will load in this same window when you click on it. The number of traces of the curve the particle makes if an overall range of \t\s is provided in the problem. Use first and second derivatives to make a rough sketch of.
Review as you will recall, the first derivative of a. Use the number line to determine where y is increasing or decreasing. Because it is a curve in 2d, it is usually easier to sketch than the graph of f. You will find it helpful to complete the step 2 calculus module first. Here is a set of practice problems to accompany the the shape of a graph, part ii section of the applications of derivatives chapter of the notes for paul dawkins calculus i course at lamar. Instead, webassign will ask limited submission questions about your graphs. This module introduces you to step questions which involve curve sketching. In separate diagrams draw sketches of the curves whose equations are.
The extreme value theorem states that a function on a closed interval must have both a minimum and maximum in that interval. Math 170 curve sketching i notes boise state university. A sketch of the parametric curve including direction of motion based on the equation you get by eliminating the parameter. Erdman portland state university version august 1, 20.
We can obtain a good picture of the graph using certain crucial information provided by derivatives of the function and certain. To start with recall the four features i look for in your sketch. In this video i discuss the following topics to help produce the graph of a function. Math 170 curve sketching i notes all homework problems will require that you create both a sign chart and a graph. Step questions are challenging, so dont worry if you get stuck. Step support programme step 2 curve sketching questions. Calculus i the shape of a graph, part ii practice problems.
Further we use this algorithm for the investigation of functions. Plot a the function is discontinuous at x 1, because ln 1 0. Curve sketching displaying top 8 worksheets found for this concept some of the worksheets for this concept are curve sketching date period, 201 103 re, curve sketching, math 1 section 006, curve sketching example, work for week 10 sketching curves, curve sketching work, work for week 3 graphs of f x and. The penguins vertical height in meters above a fixed point at time t t t minutes after starting is represented by f t. This handout contains three curve sketching problems worked out completely. Summary problems for vertical and horizontal asymptotes 7 problem.
The sketch must include the coordinates of all the points where the curve meets the coordinate axes. Determine critical points on the graph of f from the graph of f d. Pdf 12 comparison, limit comparison and cauchy condensation tests. The purpose of this collection of problems is to be an additional learning resource for students who are taking a di erential calculus course at simon fraser university. The worksheets in this packet focus on the sketching of graphs. Solutions to applications of differentiation problems pdf this problem set is from exercises and solutions written by david jerison and arthur mattuck. Detailed example of curve sketching x example sketch the graph of fx. Definition, necessary and sufficient conditions, absolute convergence. Curve sketching whether we are interested in a function as a purely mathematical object or in connection with some application to the real world, it is often useful to know what the graph of the function looks like. Although these problems are a little more challenging, they can still be solved using the same basic concepts covered in the tutorial and examples. Whether we are interested in a function as a purely mathematical object or in connection with some application to the real world, it is often useful to know what the graph of the function looks like. Curve sketching with calculus first derivative and slope second derivative and concavity.
Use your browsers back button to return to this page. Find points with f0x 0 and mark sign of f0x on number line. Here is a set of practice problems to accompany the the shape of a graph, part ii section of the applications of derivatives chapter of the notes for paul dawkins calculus i course at lamar university. In the list below, youll see some steps grouped if they are based on similar methods. Math 122b first semester calculus and 125 calculus i. Curve sketching general guidelines 1 domain of fx 2 intercepts 3 asymptotes a horizontal asymptotes lim.
A closed interval is an interval that includes its endpoints, or the points at the very. To find the x intercept, we set y 0 and solve the equation for x. No vertical asymptotes because fx continuous for all x. Learn exactly what happened in this chapter, scene, or section of calculus ab. To test your knowledge of curve sketching problems, try taking the general curve sketching test on the ilrn website or the advanced curve sketching test at the link below. Calculus curve sketching this packet contains 5 worksheets that you can use to help students work on the concept of curve sketching. Veitch 1 p x 1 0 1 p x 1 1 p x 1 x the other critical value is at x 1. You may also use any of these materials for practice. Find materials for this course in the pages linked along the left. The following steps are taken in the process of curve sketching. Click here, or on the image above, for some helpful resources from the web on this topic.
Identify clearly any interesting features, including local maximum and minimum points, inflection points, asymptotes, and intercepts. This step 2 module consists of 4 step questions, some topic notes and useful formulae, a hints sheet and a solutions booklet. Determine maximumsminimums on the graph of f from graph of f e. Apply the mean value theorem to describe the behavior of a function over an interval. Note, we did not have to pick a number in the region less than 0 since that region is not in the domain. Curve sketching rational functions exercises give a complete graph of the following functions. Ap calculus applications of derivatives math with mr. Because it is a curve in 2d, it is usually easier to sketch than. Determine the x and y intercepts of the function, if possible. Sketchingsurfacesin3d in practice students taking multivariable calculus regularly have great di. Report where this function is increasing, decreasing, or equal to zero.