2. For the function: h(x) = r³ – x² – r (a) Find the y-intercept of y = h(x), and evaluate lim h(x) and lim h(x). T -00 (b) Find h'(x), h"(x) and where they = 0. (c) Draw up a graph table for h, showing the signs of h' and h", and hence indicating where the function is increasing/decreasing and concave up/down. (d) Identify any local extrema, stating x and y coordinates and whether it is a local minimum or maximum for each. (e) Find the r and y coordinates of any points of inflection. (f) Based on the table, sketch the graph y = h(x), for the ranges -2

2. For the function: h(x) = r³ – x² – r (a) Find the y-intercept of y = h(x), and evaluate lim h(x) and lim h(x). T -00 (b) Find h'(x), h"(x) and where they = 0. (c) Draw up a graph table for h, showing the signs of h' and h", and hence indicating where the function is increasing/decreasing and concave up/down. (d) Identify any local extrema, stating x and y coordinates and whether it is a local minimum or maximum for each. (e) Find the r and y coordinates of any points of inflection. (f) Based on the table, sketch the graph y = h(x), for the ranges -2

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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