3. Algebra Worksheets Sketching Quadratic Functions Solutions 4. You da real mvps! If f00(x) = 0, the concavity is changing, so that the critical point is a point of in ection. She wants to make it to the taco truck on the beach for lunch, which is 6 miles from point A on shore (see picture). Refer again to Figure 1. Test and Worksheet Generators for Math Teachers. All worksheets created with Infinite Calculus. Printable in convenient PDF format. $1 per month helps!! If f00(x) > 0, then the graph is concave up at x. The graph of f is shown in the grid on the left. A summary of Curve Sketching in class example =−2 4+3 2 X-intercepts Y-intercepts Domain (typically all real numbers…unless a rational function) Vertical asymptotes if rational Horizontal asymptotes if rational (or end behavior if not rational) Symmetry (is f(x)=f(-x) or is f(x)= -f(x) or neither) First derivative…AND critical points First Derivative: Review As you will recall, the first derivative of a function gives you the slope, which can tell you whether the function is increasing, decreasing, or leveled off. Curve :) https://www.patreon.com/patrickjmt !! If f00(x) < 0, then the graph is concave down at x. Let’s put it all together; here are some general curve sketching rules: Find critical numbers (numbers that make the first derivative 0 or undefined). For 1 & 2, use all your math skills to analyze and sketch the graphs of the following functions. Domain -- find it. Intercepts 3. Brooke can paddle 2 miles/hour and walk 4 miles/hour. Calculus Name_ ID: 1 ©U Y2]0x1[5e OK`uJtAaR OSVoufRtIwnaRrre] ]LMLLCr.^ J TAulJlu BrXitgqhItTsq LrfeJsdeKrnv\eydE. Incorporates the use of GeoGebra and the Casio fx-991EX Classwiz. Extrema and Sketching Math 1000 Worksheet Fall 2017 Note: For practice only; not to be submitted. Sketch the graph of the curve with equation y x x x= + + −(1 4 2)( )( ), x∈ . Point C is not a turning point because, although the graph is flat for a short time, the curve continues to go down as we look from left to right. Intercepts – f(0), and those values of x – the roots – such that f(x)=0 4. Lesson 0 - Unit 3 Outline Curve Sketching Lesson 1 - Extreme Value Theorem Lesson 2 - Curve Sketching and First Derivative Lesson 3 - Curve Sketching and Second Derivatives Lesson 4 - Algorithm for Curve Sketching Lesson 5 - Optimization Problems (Area and Volume) graph Question 2 Sketch the graph of the curve with equation y x x= + −( )( )4 1 2, x∈ . 5.5: Asymptotes and Other Things to Look For. Curve Sketching: General Rules. Sketch (Using the Vertex Form Method) joint them with a smooth curve. Week 6: Midterms, Trig, and Chain Rule 23 September 2012 (Sun) Midterm Review #1 at 1pm; 24 September 2012 (M): Quiz and Questions 24 September 2012 (M) Midterm Review #2 at 6:30pm; 25 September 2012 (T) Midterm #1 MAC2311 Name: _____ Worksheet Curve Sketching Directions: Work in your small group to complete this worksheet. Curve Sketching with Calculus • First derivative and slope • Second derivative and concavity. Notice that at points A and B the curve actually turns. Problems 3 & 4. Put the critical numbers in a sign chart to see where the first derivative is positive or negative (plug in the first derivative to get signs). Identify clearly any interesting features, including local maximum and minimum points, … We will use what we have learned about 1. The following web sites will allow you to practice graphing the derivative of a function. She wants to make it to the taco truck on the beach for lunch, which is 6 miles from pointA on shore (see picture). Be sure to Title: Worksheet 2 – Curve Sketching – Solutions Author: pschaefer Last modified by: pschaefer Created Date: 1/13/2012 3:52:00 PM Company: NPSD Other titles: Thanks to all of you who support me on Patreon. So, all turning points are stationary points. Sketch the curves. The second derivative is a help with curve sketching as it tells about the concavity of the graph at any point - this is most useful at critical points. 6.Use the number line to determine where y is increasing or decreasing. If she paddles Pertinent aspects of the graph to include (include as many as you can): asymptotes (vertical/horizontal) domain local extrema/regions of increase/decrease Pre-Algebra Worksheets. SECTION 3.2: CURVE SKETCHING RATIONAL FUNCTIONS EXERCISES Give a complete graph of the following functions. Page 4 4. Problem 2. Curve Sketching Worksheet Name_____ ID: 1 Date_____ ©w P2Q0r1W4k uKduJtUab zSHozfVtpw\aurJeq yL^LGC^.O Y WAnljlt WrFimgRh_t_s[ OrFeQsleLrnvKezd^.-1-Given the graph of f (x), sketch an approximate graph of f' (x). Worksheet by Kuta Software LLC Calculus Curve Sketching Name_____ ©O a2B0g1D6E TK[uOt_aG YSGoHf`tFwwanrCe\ WLBLrC_.e t QADlRll erOi^ghhittsp lrhefsyejrovSezdK.-1-For each problem, find the: x and y intercepts, x-coordinates of the critical points, open intervals If your students need practice with the algebraic portion of the curve sketching process, see my Cal 2017-02-23 11:44:11 4/4 Ws9-curve sketching (4/4) Worksheet Math 124 Week 10 2. Return the completed worksheet along with the homework exercises at the beginning of next class. 7 For the equation y = 2(x 1)2 –3: (a) state the coordinates of the turning point (b) state whether it is a maximum or minimum (c) state the y-intercept (d) state if it is wider or narrower than y = x2 (e) sketch the curve. Symmetry – check for the following: o even – f(-x)=f(x) -- and odd – f(-x)=-f(x) -- functions; o functions that have symmetry about some displaced point; o periodicity. Curve Sketching - Handout/Worksheet Let us put together all the information we have learned to help us sketch graphs. Math 221 Worksheet 16 Second Derivative Test and Curve Sketching (1)Let f(x) = x4 4x3 + 4x2 10. Sketch the derivative in the grid on the right. pptx, 4.65 MB pdf, 209.26 KB A full lesson on sketching cubics, quartics and reciprocal functions. Sketching Polynomials Worksheet.notebook Subject: SMART Board Interactive Whiteboard Notes Keywords: Notes,Whiteboard,Whiteboard Page,Notebook software,Notebook,PDF,SMART,SMART Technologies ULC,SMART Board Interactive Whiteboard Created Date: 10/15/2015 12:51:26 PM Curve Sketching Worksheet 1. Worksheet 5.5—Curve Sketching Show all work on a separate sheet of paper. Domains 2. To carefully sketch k, we need to clearly indicate all the important features of the function, including: its domain, the y-intercept (x-intercepts if they’re easy to compute), intervals on which the function is Be sure to nd any horizontal and ver-tical asymptotes, show on a sign chart where the function is increasing/decreasing, concave up/concave down, and identifying (as ordered pairs) all relative extrema and in ection points. Worksheet 2 – Curve Sketching – Solutions. Curve Sketching Practice With a partner or two and without the use of a graphing calculator, attempt to sketch the graphs of the following functions. The sketch must include the coordinates of all the points where the curve meets the coordinate axes. (e) sketch the curve. Explanations should be written using complete sentences on the lines provided. 2. (2)Let f(x) = 1 x 3 x3 (a)Find the critical points of f and determine if they are maxima or minima using the second derivative test. No calculator unless otherwise stated. View curve_sketching.pdf from INTRO TO MACROECONOMICS 101 at Hoosac School. Curve Sketching Worksheet RETURN TO RESOURCE LIBRARY SUBSCRIBE TO OUR EMAIL LIST Grade: HSC Subject: Mathematics Extension 1 Resource type: Other Written by: N/A Year uploaded: 2016 Page length: 4 DOWNLOAD THE RESOURCE Resource Description. Worksheet by Kuta Software LLC Calculus Curve Sketching Name_____ ID: 1 Date_____ Period____ ©^ n2z0h1]5R TKRuLtoaM oSHo[fktJwwatrjek FLELaCn.D S vAOlDl` brQiWgDhdtYsz Urreps[evrmvfeFd`.-1-For each problem, find the: x and y intercepts, asymptotes, x … The worksheets in this packet focus on the sketching of graphs. Note, we did not have to pick a number in the region less than 0 since that region is not in the domain. Brooke is located 5 miles out at sea from a straight shoreline in her kayak. Find the critical points of f and determine if they are maxima or minima using the second derivative test. Calculus Curve Sketching This packet contains 5 worksheets that you can use to help students work on the concept of curve sketching. Academic Success Centre Created by Ming H. XU Page 3 -5 . These two stationary points are referred to as turning points. Problem 1. Curve Sketching Example for Worksheet 4.4 (Day 1) Let k(x) = x3 1 x3+1. Brooke can paddle 2 miles/hour and walk 4 miles/hour. 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. Worksheet on Curve Sketching. All answers must be justified and work shown for full credit. Algebra 1 ... Curve Sketching Comparing a Function and its Derivatives Motion Along a Line Related Rates Differentials Newton's Method 3.5 Summary of Curve Sketching Brian E. Veitch 1 p x 1 = 0 1 p x = 1 1 = p x 1 = x The other critical value is at x = 1. For additional practice on these top- ics, please see the WebAssign practice problem sets “Curve Sketching” and “Global (Absolute) Extrema”. Worksheet Math 124 Week 9 2.Brooke is located 5 miles out at sea from a straight shoreline in her kayak. Sketching Quadratic Functions Solutions 3.