Questions from College Mathematics

Q: Use Theorem 2 to find the local extrema. /

Use Theorem 2 to find the local extrema.

Q: (A) Find the local extrema of the functions /

(A) Find the local extrema of the functions (B) Discuss the local extrema of the function K(x, y) = xn + yn , where n is a positive integer.

Q: (A) Show that (0, 0) is a

(A) Show that (0, 0) is a critical point of the function g(x, y) = exy2 + x2 y3 + 2, but that the second derivative test for local extrema fails. (B) Use cross sections, as in Example 2, to decide wh...

Q: The annual labor and automated equipment cost (in millions of dollars

The annual labor and automated equipment cost (in millions of dollars) for a company’s production of HDTVs is given by where x is the amount spent per year on labor and y is the am...

Q: A store sells two brands of laptop sleeves. The store pays

A store sells two brands of laptop sleeves. The store pays $25 for each brand A sleeve and $30 for each brand B sleeve. A consulting firm has estimated the daily demand equations for these two competi...

Q: Repeat Problem 45, replacing the coordinates of B with B(

Repeat Problem 45, replacing the coordinates of B with B(6, 9) and the coordinates of C with C(9, 0). Data from Problem 45: A satellite TV station is to be located at P1x, y2 so that the sum of the s...

Q: A rectangular box with no top and two intersecting partitions (see

A rectangular box with no top and two intersecting partitions (see the figure) must hold a volume of 72 cubic inches. Find the dimensions that will require the least material.

Q: A shipping box is to be reinforced with steel bands in all

A shipping box is to be reinforced with steel bands in all three directions, as shown in the figure. A total of 150 inches of steel tape is to be used, with 6 inches of waste because of a 2-inch overl...

Q: find (′(0), ( ″(0), and determine whether f

find (′(0), ( ″(0), and determine whether f has a local minimum, local maximum, or neither at x = 0.

Q: Find each indefinite integral. Check by differentiating. /

Find each indefinite integral. Check by differentiating.