MT1710: Question Sheet 4 To be handed in: 30 October, 2018 (before 1pm, in the Maths office, McCrea Room 118). In question 3 below you need to use Mathematica. To gain the mark towards your continuous assessment it is compulsory to attach a print out of your Mathematica work to your hand-written solutions. 1. Use the guidelines given in lectures to sketch the following curves. You should identify any asymptotes, any intersections with the axes, etc. and include sufficient working to explain your sketch. A graphical calculator or Mathematica may be used to check the accuracy of your sketch but Mathematica output alone will not be deemed a sufficient answer to this question. x2 (a) y = x2 + 1 ; 3 x y = ~ 2 + 1 ; (b) (c) y = x2+x+ 1 x ; x2 +2x-8 (d) y = x2 - 2x - 8 ; (e) y=(x-a)(x-b)2(x-c), 0<a < b < c ; (f) ay2= x2(x+a), a > 0 . 2. Each diagram overleaf shows the graph of a function, together with the graphs of its first and second derivatives. Indicate which of the three graphs corresponds to the function and which to its first and second derivative, explaining your reasoning. [There is no need to give the equations of the graphs involved, or even the type of function which it represents.] The following question should be done using Mathematica, printed out and handed in as part of this week's work. If you are having trouble printing the file, Mathematica gives you the option of saving the file as a pdf, which you may find easier to print. 3. Plot the graphs of the following functions, together with their first and second deriva- tives, as in Question 2. (a) x5 - 2x2 on [-2, 2] , (b) arctan x on [-10, 10] , (c) Vx-x on [0,3] . The three graphs for each function should be outputted with a single Plot command. 1
1, 1 Figure 1 2 1 Figure 3 X Figure 5 2 y 2 - x Figure 2 Figure 4 Figure 6