Questions from General Calculus

Q: Find the equations of the tangent lines to the graph of y

Find the equations of the tangent lines to the graph of y = ln |x| at x = 1 and x = -1.

Q: Find the coordinates of the relative extreme point of y = x2

Find the coordinates of the relative extreme point of y = x2 ln x, x > 0. Then, use the second derivative test to decide if the point is a relative maximum point or a relative minimum point.

Q: Repeat the previous exercise with y = √x ln x.

Repeat the previous exercise with y = √x ln x. Exercise 29: Find the coordinates of the relative extreme point of y = x2 ln x, x > 0. Then, use the second derivative test to decide if the point is a...

Q: The graphs of y = x + ln x and y =

The graphs of y = x + ln x and y = ln 2x are shown in Fig. 6. (a) Show that both functions are increasing for x > 0. (b) Find the point of intersection of the graphs. Figure 6:

Q: Repeat Exercise 31 with the functions y = x + ln x

Repeat Exercise 31 with the functions y = x + ln x and y = ln 5x. (See Fig. 7). Figure 7: Exercise 31: The graphs of y = x + ln x and y = ln 2x are shown in Fig. 6. (a) Show that both functions are...

Q: Use the fact that at the beginning of 1998, the population

Use the fact that at the beginning of 1998, the population of the United States was 268,924,000 people and growing at the rate of 1,856,000 people per year. At the beginning of 1998, the annual consum...

Q: The graph of the function y = x2 - ln x is

The graph of the function y = x2 - ln x is shown in Fig. 8. Find the coordinates of its minimum point. Figure 8:

Q: The following function may be viewed as a composite function h (

The following function may be viewed as a composite function h (x) = f ( g (x)). Find f (x) and g (x). h(x) = 1/x3 - 5x2 + 1

Q: The function y = 2x2 - ln 4x (x > 0

The function y = 2x2 - ln 4x (x > 0) has one minimum point. Find its first coordinate.

Q: If the demand equation for a certain commodity is p = 45

If the demand equation for a certain commodity is p = 45/(ln x), determine the marginal revenue function for this commodity, and compute the marginal revenue when x = 20.