In Exercises 67–72, you will explore some functions and their inverses together with their derivatives and tangent line approximations at specified points. Perform the following steps using your CAS:


b. Solve the equation y=f(x) for x as a function of y, and name the resulting inverse function g.
67. y= √(3x-2), 2/3 ≤ x ≤ 4, x_0=3

31. The incidence of a disease (Continuation of Example 4.) Suppose that in any given year the number of cases can be reduced by 25% instead of 20%.

b. How long will it take to eradicate the disease—that is, reduce the number of cases to less than 1?

2. Express the following logarithms in terms of ln 5 and ln 7.

b. ln 9.8

In Exercises 1–4, solve for t.

2. b. e^(kt) = 10

Find the inverse of f(x)=x+b (b constant). How is the graph of f^(-1) related to the graph of f?

71. Locate and identify the absolute extreme values of cos(ln x) on [1/2, 2]

In Exercises 1–4, show that each function y=f(x) is a solution of the accompanying differential equation.

2. y' = y²

b. y = -1/(x+3)