CURVE SKETCHING a. Find the critical point(s) and inflection point(s) (if any) b. Determine the intervals on which the function is increasing or decreasing and concave up and down. c. Identify the maximum or minimum point(s). d. Sketch the graph 1. y = x2 +2 2. y= x2 + 4x +3 3. x3 4. y = 4x3 - 3x4 y = - 3 - 2x2 + 5x - 2 5. y= x4 - 2x2 6. y= -2+12x - x3 No sketching is required 7. y = x2 - 2x - 24 8. y= x3 - 27x Answers : 1. CP: x = 0 , No IP, Decreasing on (-oo, 0), Increasing on (0, co) , CU on (-00, on) , Minimum point (0,2) 2. CP: x = -2 , No IP, Decreasing on (-co, -2), Increasing on (-2, co) , CU on (-co, co) , Min point (-2,-1) 3. CP: x = 1,-5 , IP : x = -2, Decreasing on (-co, -5) & (1, co), Increasing on (-5,1) , CU on (-0o, -2) CD on (-2, oo), Minimum point (-5, - -) , Maximum point (1,-) 4. CP: x = 0 & x = 1, IP : x = 0,-, Increasing on (-co, 0) & (0,1) , Decreasing on (1, co), CU on (0.;), CD on (-co, 0) & (3, 0.), Maximum point (1,1) 5. CP: x = 0 ,x = 1&x = -1, IP : x = 1, Decreasing on (-co, -1) & (0,1) , Increasing on (-1,0) & (1, co), Maximum when x = 0, Minimum when x = -1 & x = 1 6. CP: x = 2, -2 , IP : x = 0 Decreasing on (-co, 2) & (2, co) , Increasing on (-2,2) , Minimum point (-2, -18) , Maximum point (2,14) 7. CP: x = 1 , Decreasing on (-co, 1) , Increasing on (1, co) , CU on (-co, co) Minimum point (1, -25) , No maximum point B. CP: x = 3, -3 , IP : x = 0 , Decreasing on (-3,3) Increasing on (-co, -3) & (3, co), CU on (0, co) and CD on (-co, 0), Minimum point (3, -54) , Maximum point (-3,54)