Questions from General Calculus

Q: Find the point on the line y = -2x + 5

Find the point on the line y = -2x + 5 that is closest to the origin.

Q: Find the value of x for which the rectangle inscribed in the

Find the value of x for which the rectangle inscribed in the semicircle of radius 3 in Fig. 19 has the greatest area. Figure 19:

Q: For what x does the function g(x) = 10

For what x does the function g(x) = 10 + 40x - x2 have its maximum value?

Q: Differentiate the function f (x) = (3x2 + x

Differentiate the function f (x) = (3x2 + x - 2)2 in two ways. (a) Use the general power rule. (b) Multiply 3x2 + x - 2 by itself and then differentiate the resulting polynomial

Q: Find the maximum value of the function f (x) =

Find the maximum value of the function f (x) = 12x - x2, and give the value of x where this maximum occurs.

Q: Find the minimum value of f (t) = t3 -

Find the minimum value of f (t) = t3 - 6t2 + 40, t Ú 0, and give the value of t where this minimum occurs.

Q: For what t does the function f (t) = t2

For what t does the function f (t) = t2 - 24t have its minimum value?

Q: A California distributor of sporting equipment expects to sell 10,000

A California distributor of sporting equipment expects to sell 10,000 cases of tennis balls during the coming year at a steady rate. Yearly carrying costs (to be computed on the average number of case...

Q: The Great American Tire Co. expects to sell 600,000

The Great American Tire Co. expects to sell 600,000 tires of a particular size and grade during the next year. Sales tend to be roughly the same from month to month. Setting up each production run cos...

Q: Foggy Optics, Inc., makes laboratory microscopes. Setting up each

Foggy Optics, Inc., makes laboratory microscopes. Setting up each production run costs $2500. Insurance costs, based on the average number of microscopes in the warehouse, amount to $20 per microscope...