Tutorial 1 - Curve Sketching and Max Min problems.pdf - FAM0025/FBM0045 QAII 2019 TUTORIAL 1 CURVE SKETCHING a Find the critical point(s and inflection

# Tutorial 1 - Curve Sketching and Max Min problems.pdf -...

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FAM0025/FBM0045 QAII 2019 1 2019 COMPILED BY WSWMP TUTORIAL 1 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. ? = ? 2 + 2 2. ? = ? 2 + 4? + 3 3. ? = − ? 3 3 − 2? 2 + 5? − 2 4. ? = 4? 3 − 3? 4 5. ? = ? 4 − 2? 2 6. ? = −2 + 12? − ? 3 7. ? = ? 2 − 2? − 24 8. ? = ? 3 − 27? Answers : 1. 𝐶𝑃: ? = 0 , No IP, Decreasing on (−∞, 0) , Increasing on (0, ∞) , CU on (−∞, ∞) , Minimum point (0,2) 2. 𝐶𝑃: ? = −2 , No IP, Decreasing on (−∞, −2) , Increasing on (−2, ∞) , Minimum point (−2, −1) 3. 𝐶𝑃: ? = 1, −5 , IP : ? = −2, Decreasing on (−∞, −5) & (1, ∞) , Increasing on (−5,1) , CU on (−∞, −2) CD on (−2, ∞) , Minimum point (−5, − 106 3 ) , Maximum point (1, 2 3 ) 4. 𝐶𝑃: ? = 0 & ? = 1 , IP : ? = 0 , 2 3 , Increasing on (−∞, 0) & (0,1) , Decreasing on (1, ∞) , CU on (0, 2 3 ) , CD on (−∞, 0) & ( 2 3 , ∞), Maximum point (1,1) 5. 𝐶𝑃: ? = 0 , ? = 1 & ? = −1 , Decreasing on (−∞, −1) & (0,1) , Increasing on (−1,0) & (1, ∞) , Relative maximum when ? = 0 , Relative minimum when ? = −1 & ? = 1 6. 𝐶𝑃: ? = 2, −2

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