Questions from General Calculus

Q: A car is traveling on a straight road and s(t

A car is traveling on a straight road and s(t) is the distance traveled after t hours. Match each set of information about s(t) and its derivatives with the corresponding description of the car’s moti...

Q: The water level in a reservoir varies during the year. Let

The water level in a reservoir varies during the year. Let h(t) be the depth (in feet) of the water at time t days, where t = 0 at the beginning of the year. Match each set of information about h(t) a...

Q: Let f (x) be the number of people living within

Let f (x) be the number of people living within x miles of the center of New York City. (a) What does f (10 + h) - f (10) represent? (b) Explain why f ‘(10) cannot be negative.

Q: For what x does the function f (x) = 1

For what x does the function f (x) = 1/4 x2 - x + 2, 0 ≤ x ≤ 8, have its maximum value?

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

Find the maximum value of the function f (x) = 2 - 6x - x2, 0 ≤ x ≤ 5, and give the value of x where this maximum occurs.

Q: Find the minimum value of the function g(t) =

Find the minimum value of the function g(t) = t2 - 6t + 9, 1 ≤ t ≤ 6.

Q: The tangent line to the curve y = x3 - 6x2 -

The tangent line to the curve y = x3 - 6x2 - 34x - 9 has slope 2 at two points on the curve. Find the two points.

Q: An open rectangular box is to be 4 feet long and have

An open rectangular box is to be 4 feet long and have a volume of 200 cubic feet. Find the dimensions for which the amount of material needed to construct the box is as small as possible.

Q: A closed rectangular box with a square base is to be constructed

A closed rectangular box with a square base is to be constructed using two different types of wood. The top is made of wood costing $3 per square foot and the remainder is made of wood costing $1 per...

Q: A long rectangular sheet of metal 30 inches wide is to be

A long rectangular sheet of metal 30 inches wide is to be made into a gutter by turning up strips vertically along the two sides (Fig. 6). How many inches should be turned up on each side to maximize...