 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). 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: 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: 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: 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: 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: A woman at a point A on the shore of a circular

A woman at a point A on the shore of a circular lake with radius 2 mi wants to arrive at the point C diametrically opposite A on the other side of the lake in the shortest possible time (see the figur...