Exam 14: Curve Sketching

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

A manufacturer has to produce annually 360 units of a product that are sold at a uniform rate during the year.The production cost for each unit is $200,and carrying costs (insurance,interest,storage,and so on)are estimated to be 10% of the value of average inventory.Set-up costs per production run are $100.Find the economic lot size.

A cable TV company has 500 customers paying $20 each month.For each $1 reduction in price,the company attracts 50 more customers.Find the price that yields maximum revenue.

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

A released film has a revenue given by R(t)= ,where R(t)is in millions of dollars and t is the number of weeks after its release.Sketch the graph of this function.

A drug is injected into a patient's bloodstream.The concentration of the drug in the bloodstream t hours after the injection is approximated by C(t)= .Find the relative extrema and use this to determine when the drug is at its greatest concentration.

If C = -4x + is a cost function,sketch the graph of this function with the aid of intercepts,symmetry,and the first-derivative test.

The cost equation for a company is C(x)= + 5 - 8x + 250.Use the second-derivative test,if applicable,to find the relative maxima and the relative minima.

Use the second derivative test to find the points of relative maxima and relative minima for the function

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

On the interval ,the function y = - Has

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

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)= - 7 + 2x - 5,then f is concave down on the interval

Determine the intervals on which the function is increasing and on which it is decreasing.Also determine the points of relative maxima and relative minima. f(x)= 16 - 5x

If C = 4x - 5 + is a cost function,sketch the graph of this function with the aid of intercepts,symmetry,and the first-derivative test.

Let f(x)= 3 - 10 + 7x.Determine the intervals on which f is (a)concave up and (b)concave down. (c)Find the x-values of all inflection points.

The revenue equation for a company is given by R(x)= 1296x - 0.12 .Determine when relative extrema occur on the interval (0,∞).

Suppose that the total number of units produced by a worker in t hours of an 8-hour shift can be modeled by the production function P(t)= 20t + 15 - .Find where the function is concave up and where the function is concave down.

The revenue equation for a company is given by R(x)= 84.375x - 0.5 .Determine when relative extrema occur on the interval (0,∞).