Chapter 10.2, Problem 22E

Use the mapping rule to transform the parent function y=x5 to f(x)= 5/96(x+2)(x-1/2)(x+1)3.   The mapping rule involves transforming the y=x5 table of values into a new table of values for f(x). The mapping rule is x/k+d to transform x values, and ay+c to transform y values in the general form y=af(k(x-d))+c. Please include both tables of values for the transformation.

Let f(a, y) = 3x² + 4y2 – axy. (a) Find the values of a such that the graph of f increases when moving from the point (1, 2) in the positive x-direction. (b) Find the values of a such that the graph of f increases when moving from the point (1, 2) in the positive y-direction.

Find all analytic functions f = u + iv with u(x, y) = x² - y². Simplify the expression f(2) as much as possible.

Let Y1, Y2, ..., Y, denote a random sample from the probability density function --. f(y[@) = 0, elsewhere. Show that Y(1) = min(Y, Y2,..., Y,) is sufficient for e.