Exam 14: Curve Sketching

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

The demand equation for a monopolist's product is p = ,where p is the price per unit (in dollars)when q units are demanded. (a)Determine the value of q for which revenue is maximum. (b)What is the maximum revenue?

Let y = - 3 - 9x + 10. (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.

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.

Using fencing,a rectangular area is to be enclosed next to the wall of a building.The building will form one of the sides and no fencing will be placed there.The cost of the fencing for the side opposite the building is $5 per foot.The cost of the fencing for the other two sides is $3 per foot.The area to be enclosed is 3000 .In order to keep expenses of the three sides to a minimum,how many feet of each type of fencing must be bought?

If f(x)= 2 + 3 - 36x + 1,determine the intervals on which f is increasing and the intervals on which f is decreasing.

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

If y = + 4 - 18 - 3x + 4,find the x-values of all inflection points.

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

Given y = f(x)= - 3 + 10 on the interval ,find the values of x at which absolute maxima and absolute minima occur.

The revenue equation for a company is given by R(x)= 173.28x - 0.16 .Determine when relative extrema occur on the interval (0,∞).

If y = 3 - 6 ,use the second-derivative test to find all values of x for which (a)relative maxima occur (b)relative minima occur.

The cost equation for a company is C(x)= 2 - 39 + 180x + 21,200.Use the second-derivative test,if applicable,to find the relative maxima and the relative minima.

If y = x(x - ,find the x-values of all inflection points.

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)=

It is estimated that under a short-term energy-assistance plan,n million households will receive direct aid in meeting home-fuel costs after t years,where For what value of t will n be a maximum?

Sketch the graph of y = - 4x with the aid of intercepts,symmetry,and the first-derivative test.Use your Graphing Calculator to verify your solution.

Let f(x)= x(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.

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)= 19t + - .Find where the function is concave up and where the function is concave down.

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)=