Assume that you have a function f defined on [0, 1], and you compute f(x) for values of x that are separated by 0.1. You get the following values: f(0) = 4, f(0.1) = 3.1, f(0.2) = 1.9, f(0.3) = 0.7, f(0.4) = −0.4, f(0.5) = −1.3, f(0.6) = −2, f(0.7) = −2.1, f(0.8) = −1.7, f(0.9) = −0.6, f(1) = 1.3 Use these values to draw the graph of f as precisely as possible (use a ruler!).
If you only have access to the values above, how would you guess the global extrema
of f? Are these the actual extrema of f? Why or why not?
Now, assume that you have a function of two variables defined on the square

D = {(x, y) : 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}.

Once again, you want to compute enough values of f(x, y), with (x, y) separated by
0.1 on a grid pattern. In other words, you compute f(x, y) for
(x, y) = (0, 0),(0.1, 0),(0, 0.1),(0.2, 0), . . . ,(1, 1).

How many values do you need to compute?
Generalize to a function of n variables where each variable is in [0, 1].
Give a numerical application for the previous question for n = 3, n = 10, n = 20,
n = 100. Write your result in scientific notation with one significant digit.
How does the result of Question 4 change if we instead want the variables separated
by 0.01? Just give the results, no need to explain. Then give a numerical application
as in the previous question.
The current fastest supercomputer can do 1018 operations per second. Compare to
Questions 5 and 6, and comment. Cultural note: in practice, functions can have
millions of variables or more!