Exercises

The unit closes with a few simple exercises for you to test the skills you have learned throughout the unit.

Question

Problem 1: Hint based problem

Write functions to calculate the maximum and minimum of an array of numbers, without using the commands max or min. Your functions should take in a vector and return values for the maximum and minimum.

Expand for hint

Hint

The following if statement will find the maximum between max_x and x(i):

if x(i)>max_x
    max_x=x(i);
end

Combine the functions from part 1. to make one function that returns both the maximum and the minimum. See doc function for help on how to return multiple values.

Expand for solution

Solution

The following code will calculate the maximum of an array passed to it:

function [max_x] = maximum(x)
    max_x=x(1);
    for i=1:length(x)
        if x(i)>max_x
            max_x=x(i);
        end
    end

The following code will calculate the minimum of an array passed to it.

function [min_x] = minimum(x)
    min_x=x(1);
    for i=1:length(x)
        if x(i)<min_x
            min_x=x(i);
        end
    end

To use these, save the above a .m files with the appropriate names, and run the commands:

minimum(x)
maximum(x)

where x is a vector.

The following code will calculate the minimum and the maximum of an array passed to it:

function [min_x,max_x] = minmax(x)
    min_x=x(1);
    max_x=x(1);
    for i=1:length(x)
        if x(i)<min_x
            min_x=x(i);
        end
        if x(i)>max_x
            max_x=x(i);
        end
    end

To call the function, save the above as minmax.m, and run:

[minimum,maximum] = minmax(x)

Question

Problem 2: Hint based problem

Plot the functions $y=x^3$ and $y=x^5$ , on the interval $[-2,\,2]$ , on the same graph. Where are the intersections of the curves?

Expand for hint

Hint

You may want to create the following vectors:

x=linspace(-2,2,100);
y1=x.^3;

and use the plot functionality you learned in this unit.

Add a title and legend to the graph, label the axes, and save the figure as a .png file.

Expand for solution

Solution

Intersections occur at $(x,\,y)=(−1,\,−1),(0,\,0),(1,\,1)$ . The following commands plot the curves:
```
x=linspace(-2,2,100);
y1=x.^3;
y2=x.^5;
plot(x,y1,'-',x,y2,'--');
```
The following commands will add a label and legend to the figure:
```
legend('y=x^3','y=x^5');
xlabel('x');
ylabel('y');
```
You can save the file by using ‘Save As’ in the ‘File’ menu or by using the following command.
```
print ExampleFigure.png -dpng
```