Exam 14: Curve Sketching

Let f(x)= . (a)Determine the intervals on which f is increasing. (b)Determine the intervals on which f is decreasing. (c)Based on your answers to parts (a)and (b),find the values of x for which f has relative maxima. (d)Based on your answers to parts (a)and (b),find the values of x for which f has relative minima.

If f(x)= (x + 4),then f has an inflection point when x =

If C = -3x - 2 + is a cost function,sketch the graph of this function with the aid of intercepts,symmetry,and the first-derivative test.

The demand equation for a monopolist's product is p = ,where p is the price per unit (in dollars)for q units.If the total cost c (in dollars)of producing q units is given by c = 5q+ 2000,then the level of production at which profit is maximized is

The cost equation for a company is C(x)= 3 - 27 + 45x + 100.Use the second-derivative test,if applicable,to find the relative maxima and the relative minima.

A cable TV company has 200 customers paying $10 each month.For each $1 reduction in price,the company attracts 50 more customers.Find the price that yields maximum revenue.

Use the second derivative test to find the relative extremas of f(x)= 10x and where they occur.If the relative extremas can not be determined by the second derivative test,state so.

A manufacturer has determined that the total cost c of producing q units of a product is given by Average cost will be a minimum at a production level of

Given y = f(x)= 2 +12 - 7 on the interval ,find the values of x at which absolute maxima and absolute minima occur.

The demand function for a monopolist's product is p = 100 - 3q,where p is the price per unit (in dollars)for q units.If the average cost (in dollars)per unit for q units is = 4 + ,find the output q at which profit is maximized.

Find all the critical values of f(x)= 12 - 65 + 45x + 60.

The function y = + 15 - 33x has a relative maximum when x =

Let f(x)= + 5 .Determine the intervals of which f is (a)concave up and (b)concave down.(c)Find the x-values of all inflection points.

The function f(x)= is concave down on the interval(s)

If f(x)= - - 15x - 7,determine the intervals on which f is increasing and the intervals on which f is decreasing.

Determine the equations of the vertical asymptotes and non-vertical asymptotes for the graph of

Determine the equations of the vertical asymptotes and non-vertical asymptotes for the graph of

Let f(x)= . (a)Determine the intervals on which f is increasing. (b)Determine the intervals on which f is decreasing. (c)Based on your answers to parts (a)and (b),find the values of x for which f has relative maxima. (d)Based on your answers to parts (a)and (b),find the values of x for which f has relative minima.

Find the intervals where the graph of y = f(x)is concave up and where it is concave down.Do not sketch its graph.Also determine its points of inflection.f(x)= - + 5.

If f(x)= - ,determine the intervals on which f is increasing and the intervals on which f is decreasing.