Math 111H: MATLAB Assignment 2

Implicit Differentiation


Due Date: November 30, 2007



Let's revisit implicit differentiation. In this exercise, we will also learn to use matlab symbolically. Consult the MATLAB TA's if you have any questions. Hand in all figures.


Let us use the ezplot command to draw the graph of the equation
x2+y2=25


by entering in matlab:


>> ezplot('x^2 + y^2 - 25',[-6 6],[-6 6])


Since the curve does not look like a circle, you may want to enter

>> axis square



Even though the graph is not the graph of a function, we can zoom in to a particular neighborhood of a point, say, (4,3) by entering


>> axis([ 1 5 1 5])


And now the figure looks like the graph of a function.  In class, we showed that the equation of the tangent line to the graph at (4,3) is

y=-(4/3) (x-4) +3

which can be rewritten as

-(4/3)(x-4) + 3 - y = 0

Let us now plot the tangent line on the same graph by entering:

>> hold on
>> ezplot('-(4/3)*(x-4)+3-y' , [-6 6],[-6 6]);


What do you see now?  What happens when you zoom back out to see the whole graph by entering:

>> axis([-6 6 -6 6])



Now let us plot the two curves
5y-2x+y3-x2y=0
2y+5x+x4-x3y2=0

Show that the two curves intersect at right angles at the origin (by plotting the two tangents and showing that the tangents are at right angles to each other).