Questions from General Calculus

Q: Find an equation of the line through the point (3,

Find an equation of the line through the point (3, 5) that cuts off the least area from the first quadrant.

Q: Let a and b be positive numbers. Find the length of

Let a and b be positive numbers. Find the length of the shortest line segment that is cut off by the first quadrant and passes through the point (a, b).

Q: At which points on the curve y = 1 + 40x3 -

At which points on the curve y = 1 + 40x3 - 3x5 does the tangent line have the largest slope?

Q: What is the shortest possible length of the line segment that is

What is the shortest possible length of the line segment that is cut off by the first quadrant and is tangent to the curve y = 3/x at some point?

Q: What is the smallest possible area of the triangle that is cut

What is the smallest possible area of the triangle that is cut off by the first quadrant and whose hypotenuse is tangent to the parabola y = 4 - x2 at some point?

Q: (a) If C(x) is the cost of

(a) If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) = C(x)/x. Show that if the average cost is a minimum, then the marginal cost equals the average cost...

Q: (a) Show that if the profit P(x)

(a) Show that if the profit P(x) is a maximum, then the marginal revenue equals the marginal cost. (b) If C(x) = 16,000 + 500x - 1.6x2 + 0.004x3 is the cost function and p(x) = 1700 - 7x is the demand...

Q: A baseball team plays in a stadium that holds 55,000

A baseball team plays in a stadium that holds 55,000 spectators. With ticket prices at $10, the average attendance had been 27,000. When ticket prices were lowered to $8, the average attendance rose t...

Q: During the summer months Terry makes and sells necklaces on the beach

During the summer months Terry makes and sells necklaces on the beach. Last summer he sold the necklaces for $10 each and his sales averaged 20 per day. When he increased the price by $1, he found tha...

Q: A retailer has been selling 1200 tablet computers a week at $

A retailer has been selling 1200 tablet computers a week at $350 each. The marketing department estimates that an additional 80 tablets will sell each week for every $10 that the price is lowered. (a)...