Exam 14: Curve Sketching

Let y = - 3 (a)Find y' and y''. (b)Determine intervals on which the function is increasing; determine intervals on which the function is decreasing. (c)Determine the coordinates of all relative maximum and relative minimum points. (d)Determine intervals on which the function is concave up; determine intervals on which the function is concave down. (e)Determine the coordinates of all inflection points. (f)With the aid of the information obtained in parts (a)- (e),give a reasonable sketch of the curve.

The graph of a function is given.Find (a)the open intervals on which the function is increasing or decreasing; (b)the coordinates of all relative extrema.

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

Find the vertical and non-vertical asymptotes of the following function.Do not sketch its graph. y =

Use your graphing calculator to graph y = ln(x)+ .Inspect the graph to estimate where the relative extrema occur.Then use the first-derivative test to find the relative extrema.

Find two positive numbers whose product is 25 and whose sum is a minimum.

Let f(x)= .Find the x values of (a)all relative maxima,(b)all relative minima,and (c)all inflection points.

Use your graphing calculator to graph f(x)= - + 2.Looking at the graph,estimate the intervals where the function is concave up and concave down.Now find these intervals using the second derivative.

You have been asked to design a rectangular box with a square base and lid.The volume of the box must be The cost per square foot of material for the base is $0.50,for the sides $0.20,and for the lid $0.10.If the total cost of materials is a minimum,then the dimensions (in feet)of the box are

A company owns an apartment building containing 100 units.If the company charges $400 per month rent,then all units can be rented out,and for every increase of $20 per month in rent,the company will lose one customer.What rent should be charged to maximize revenue?

The cost equation for a bakery is given by C(x)= 10(x - - 120(x - 2)+ 450,where x is the number of doughnuts made (in dozens),and C(x)is the cost in dollars.Use the first-derivative test to find when relative extrema occur.

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

A rectangular closed box with a square base is to have a volume of 1000 .Find its dimensions if the box is to require the least possible material.

An equation of a horizontal asymptote for the graph of y = is

An equation of a vertical asymptote for the graph of y = is

Let y = - 4 . (a)Determine y' and y''. (b)Determine intervals on which the function is increasing; determine intervals on which the function is decreasing. (c)Determine the coordinates of all relative maximum and relative minimum points. (d)Determine intervals on which the function is concave up; determine intervals on which the function is concave down; (e)Determine the coordinates of all inflection points. (f)With the aid of the information obtained in parts (a)-(e),give a reasonable sketch of the curve.

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

A manufacturer found that the total cost c of producing q units of a product is given by At what level of production will average cost be a minimum?

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)= 16 - 5x.

Use your graphing calculator to estimate the relative extrema of the function (estimate to 3 decimal places).