Chapter 4, Lesson 1 Curve Sketching Complete this assignment by hand and do not type your answers. You may NOT use a graphing calculator to determine the shape ofthe graph, but you may use a calculator for basic arithmetic to help you find values of the function. Make sure you are showing all your steps clearly. when you upload your work into the LMS, make sure your work is vertical so it can be easily viewed and graded. Follow the 5 Steps for Curve Sketching to sketch the graph ofthe function. (20 points) 3 x) =x?x23x Step 1: Find the critical points and plot them on the graph on the next page. a. Find the first derivative. b. Set the first derivative equal to O and find where the first derivative does not exist. c. Plug the xvalue of each critical point into the original function to find the yvalue of the point itself. m!"- D @I 7 '? "@i Step 2: Use the table below to test the regions to see where the function increases or decreases. Include your work for determining the sign of each interval. mm...) (Steps continued on the next page) Step 3: Find the possible inflection points and plot them on the graph below. a. Find the second derivative. b. Set the second derivative equal to O and find where the second derivative does not exist. c. Plug the x-value of each possible point of inflection into the original function to find the y-value of the point itself. Step 4: Use the table below to test for the concavity of the function. Include your work for determining the sign of each interval. Behavior of f(x) Step 5: Sketch the curve. y Follow the 5 Steps for Curve Sketching to sketch the graph of the function. (20 points) 2x3 2 .905) =7 Step I: Find the critical points and plot them on the graph below. Step 2: Use the table below to test the regions to see where the function increases or decreases. Include your work for determining the sign of each interval. Intervals Step 3: Find the possible inflection points and plot them on the graph below. Step 4: Use the table below to test for the concavity ofthe function. Include your work for determining the sign of each interval. Step 5: Sketch the cu rve. y Step 4: Use the table below to test for the concavity of the function. Include your work for determining the sign of each interval. Step 5: Sketch the curve. y Part 3: Oh no! While you were working on your calculus homework at your favorite coffee shop, you accidentally spill your coffee on your paper. The coffee spilled all over the equations for the function and its derivatives, but thankfully the rest of yourwork was saved. Using the information below, sketch the graph of h(x)_. (10 points) '10:) = , >5}: h'Ot): Slay) . 1 1 Mg) = .L K h'(x): Critical points at x = 4, x = 1,x = 3 h"(x): Possible inflection points atx = 4,x = 1,x = 3 Points: h(4) = O;h(1)= 3; h(1) = 8; M3) is undefined; ME) = 2 SgSiiigi