Presentation exercises are marked with a *.²
Review problems, page 157, Exercises 9,12,24,27,32,33,48,49,50.
Practice problems, page 163, Exercises 1, 5, 10, 15, 20, 25, 30, 35, 40, 45,46* , 50, 55, 60.
Graphing exercises: for each of the following functions, compute the first and second derivatives. Find out on what intervals the function is increasing/decreasing and on what intervals the function is concave up/ concave down. Calculate the local maxima and minima, and the points of inflection (points where the concavity changes). Consider what happens the the function for large positive and negative values of x. On the basis of all this information, draw a sketch of the function, with the several important points labelled -- i.e. the local maxima and minima, and the points of inflection. Finally, get Mathematica to make a plot of the function and compare the computer plot with your sketch.
a) f(x) = 5 x^3 - 12 x^2 + 2x - 3
b) f(x) = x exp(-x). (Presentation exercise!)
Do this Mathematica exercise, which involves parameter estimation for the mathematical model of intramuscular injection which was presented last week in lecture. To prepare, read thru the Mathematica demonstration injection_model.nb. Then work through the questions in the Mathematica notebook injection_project.nb. (Presentation exercise!)