Exam 8: Calculus of Several Variables

Find the critical point(s) of the function.Then use the second derivative test to classify the nature of each point, if possible.Finally, determine the relative extrema of the function. Find the critical point(s) of the function. Find the point(s) of maximum. Find the point(s) of minimum. Find the relative extrema of the function.

The IQ (itelligence quotient) of a person whose mental age is years and whose chronological age is years is defined as What is the IQ of a 10-years-old child who has a mental age of 19 years?

Find the critical point(s) of the function.Then use the second derivative test to classify the nature of each point, if possible.Finally, determine the relative extrema of the function. Find the critical point(s) of the function. Find the point(s) of maximum. Find the point(s) of minimum. Find the relative extrema of the function.

An open rectangular box is to be constructed from material that costs for the bottom and for its sides.Find the dimensions of the box of greatest volume that can be constructed for .

Determine whether the statement is true or false.If it is true, explain why it is true.If it is false, give an example to show why it is false. If h(x, y) = f(x)g(y), where f is continuous on [a, b] and g is continuous on [c, d], then where

Sketch the domain of the function.

Find the domain of the function. f(u, v) = ln(u + v - 6)

Evaluate the double integral for the function and the region R. and R is the rectangle defined by and .

Because of new, lower standards, experts in a study conducted in early 2000 projected a rise in the market for cholesterol-reducing drugs.The any market (in billions of dollars) for such drugs from 1999 through 2004 is given in the following table ( represents 1999): Find an equation of the least-squares line for these data.Please round coefficients to the nearest hundredth if necessary.Estimate the market for cholesterol-reducing drugs in 2005, assuming the trend continued.

Find the equation of the least-squares line for the given data.Draw a scatter diagram for the given data and graph the least-squares line. Please round the coefficients in your equation to two decimal places.

Find the critical point(s) of the function.Then use the second derivative test to classify the nature of each point, if possible.Finally, determine the relative extrema of the function.

Use a double integral to find the volume of the solid shown in the figure.

Postal regulations specify that the combined length and girth of a parcel sent by parcel post may not exceed 132 in.Find the dimensions of the rectangular package that would have the greatest possible volume under these regulations.(Hint: Let the dimensions of the box be by by (see the figure below).Then, , and the volume .So that .Maximize .) x = __________ inches y = __________ inches z = __________ inches V = __________ cubic inches

Maximize the function subject to the constraint .

Evaluate the double integral for the function and the region . and is bounded by , , and .

Evaluate the first partial derivatives of the function at the given point.

Maximize the function subject to the constraints .

A closed rectangular box having a volume of is to be constructed.If the material for the sides costs and the material for the top and bottom costs , find the dimensions of the box that can be constructed with minimum cost.

Evaluate the double integral for the given function f(x, y) and the region R. f(x, y) = 5 ; R is bounded by the lines x = 1, y = 0 and y = x.

In a survey it was determined that the demand equation for VCRs is given by The demand equation for blank VCR tapes is given by where and denote the unit prices, respectively, and and denote the number of VCRs and the number of blank VCR tapes demanded each week.Determine whether these two products are substitute, complementary, or neither.