Questions from General Calculus

Q: The sum of two positive numbers is 16. What is the

The sum of two positive numbers is 16. What is the smallest possible value of the sum of their squares?

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: Produce graphs of f that reveal all the important aspects of the

Produce graphs of f that reveal all the important aspects of the curve. In particular, you should use graphs of f' and f" to estimate the intervals of increase and decrease, extreme values, intervals...

Q: Produce graphs of f that reveal all the important aspects of the

Produce graphs of f that reveal all the important aspects of the curve. In particular, you should use graphs of f' and f" to estimate the intervals of increase and decrease, extreme values, intervals...

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

(a). If C (x) is the cost of producing 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 co...

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 dem...

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 manufacturer has been selling 1000 television sets a week at $

A manufacturer has been selling 1000 television sets a week at $450 each. A market survey indicates that for each $10 rebate offered to the buyer, the number of sets sold will increase by 100 per week...

Q: The manager of a 100-unit apartment complex knows from experience

The manager of a 100-unit apartment complex knows from experience that all units will be occupied if the rent is $800 per month. A market survey suggests that, on average, one additional unit will rem...