Exam 4: Analyzing Change: Applications of Derivatives

Given the units of measure for production and the units of measure for cost or revenue. Write the units of measure for the indicated marginal. Total cost is given by million dollars when q million units are produced; .

Find the derivative of the function.

Find the relative minima, and use a graphing utility to check your results.

The figure shows an estimate of the ultimate crude oil production recoverable from Earth. Estimate the two inflection points on the graph.

Write a model for the output variable in terms of one input variable. A rectangular-shaped garden has one side along the side of a house. The other three sides are to be enclosed with 60 feet of fencing. What is the largest possible area of such a garden?

Rewrite the statement into equivalent statement without using the term marginal. At a production level of 500 units, marginal cost is $17 per unit.

If and , estimate .

The percentage of southern Australian grasshopper eggs that hatch as a function of temperature (for temperatures between 7°C and 25°C) can be modeled as where t is the temperature in °C, data from What temperature between 7°C and 25°C corresponds to the least percentage of eggs hatching? What is the percentage at this input?

During the summer, an art student makes and sells necklaces at the beach. Last summer she sold the necklaces for $10 each and her sales averaged 20 necklaces per day. When she increased the price by $1, she found that she lost 2 sales per day. Assume that this pattern would continue if she kept increasing the price; that is, for every dollar she raised the price, she would sell 2 fewer necklaces per day. Write a model for the student's daily revenue from the sale of x necklaces.

The amount of water an oak tree can remove from the ground is related to the tree's size. Suppose that an oak tree transpires where g is the girth in feet of the tree trunk, measured 5 feet above the ground. A tree is currently 5 feet in girth and is gaining 2 inches of girth per year. If t is time measured in years, evaluate