Use the derivative to find the vertex of the parabola.y = -2×2 + 12x – 3

Solve the problem.Barbara knows that she will need to buy a new car in 5 years. The car will cost $15,000 by then. How much should she invest now at 6%, compounded quarterly, so that she will have enough to buy a new car? Round to the nearest cent.

Solve the problem.Bob owns a watch repair shop. He has found that the cost of operating his shop is given by , where x is the number of watches repaired. What is his minimum cost?

Solve the problem.Suppose that the total profit in hundreds of dollars from selling x items is given by Find the marginal profit at x = 1.

Find all the critical numbers of the function.f(x) = x3 + x2 – 27x + 2

Calculate the absorption rate constant of the drug. For your calculation of KE use the 20 and 24 hr. time points.  During the “feathering” process for your calculation of ka use the 1 and 2 hour time points.

Calculate the volume of distribution (Vd).

Use the following information to answer the remaining questions.  The drug is administered orally. Dose = 150 mg CL = 5.625 L/hr F = 0.8 Time (hrs) Cp (mg/L) 0 0.000 0.5 0.807 1 1.312 1.5 1.614 2 1.778 3 1.862 5 1.638 7 1.317 10 0.915 12 0.714 16 0.433 20 0.263 24 0.159

Find the equation of the secant line through the points where x has the given values.f(x) = x2 + 4x; x = 5, x = 2

Solve the problem.The total cost to produce x units of perfume is Find the marginal average cost function.