MATH 164, Spring 2001 Due Date: Name(s):
Extra Project 7.4d: Exponentials, Logarithms, and Their Derivatives
Objective
To compare the behavior of various exponential and logarithmic functions, and their derivatives.
Narrative
If you have not already done so, read Section 7.4 in the text.
In this project you will differentiate and use the plot command to plot several exponential and logarithmic
functions on one set of coordinate axes.
Tasks
1. Type the command lines below into Maple in the order in which they are listed. These commands
produce graphs of various exponential and logarithmic functions, and their derivatives.
> # Project 7.4d: Exponentials, Logarithms, and Their Derivatives
> restart;
> f := x -> sin(x)+ln(x);
> diff(f(x),x);
> plot({f(x),diff(f(x),x)},x=-10..10,y=-10..10);
> f := x -> ln(x^2+x+1);
> diff(f(x),x);
> plot({f(x),diff(f(x),x)},x=-10..10,y=-10..10);
> f := x -> ln(2*x+x*sin(x));
> diff(f(x),x);
> diff(f(x),x,x);
> plot({f(x),diff(f(x),x),diff(f(x),x,x)},x=-10..10,y=-10..10);
> f := x -> exp(sin(5*x));
> diff(f(x),x);
> plot({f(x),diff(f(x),x)},x=-2..2);
> f := x -> exp(x)/(1+x);
> diff(f(x),x);
> plot({f(x),diff(f(x),x)},x=-5..5,y=-5..5);
At this time, make a hard copy of your typed input and Maple's responses. Then, ...
2. Label by hand each of the curves in each of the graphics you created in part (1).