Chapter 10.2, Problem 23E

Assume that functions ƒ and g are differentiable with ƒ(2) = 3, ƒ′(2) = -1, g(2) = -4, and g′(2) = 1. Find an equation of the line perpendicular to the graph of F(x) = (ƒ(x) + 3) /(x - g(x))  at x = 2.

Find the linearization L(x) of the function f(x)=x to the 4th power +2x to the 2nd power +1 at x=2. Answer: L(x)=

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.

The function f(x) is everywhere continuous and differentiable. Prove that if the function f(x) has two real roots, then its derivative f′(x) has at least one root.

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.