Exam 4: Graphing and Optimization

Solve the problem. -A local office supply store has an annual demand for 50,000 cases of photocopier paper per year. It costs $1 per year to store a case of photocopier paper, and it costs $50 to place an order. Find the optimum number of cases Of photocopier paper per order.

Provide an appropriate response. -Find two numbers whose sum is 360 and whose product is a maximum.

Sketch a graph of a single function that has these properties. -a) Continuous and differentiable for all real numbers b) c) d) e) f) g) An inflection point at (0,0)

Sketch the graph and show all local extrema and inflection points. -

Sketch a graph of a single function that has these properties. -Determine the interval(s) over which is concave downward.

Sketch a graph of a single function that has these properties. -Find

Provide an appropriate response. -Find horizontal asymptotes, if any, for

Find the intervals where f''(x) < 0 ir f''(x) > 0 as indicated. -

Find the limit, if it exists. -Find

Provide an appropriate response. -Find the absolute minimum value of f(x) = 4x ln x - 7x. Round your answer to three decimal places.

Provide an appropriate response. -Suppose that the total-cost function for a certain company to produce x units of a product is given by Graph the average cost function

Sketch a graph of a single function that has these properties. -Find

Sketch a graph of a single function that has these properties. -Find

Provide an appropriate response. -Find the absolute minimum value of

Solve the problem. -A company estimates that it will sell N(t) hair dryers after spending $t thousands on advertising as given by: For which values of t is the rate of sales N'(t) in creasing?

Solve the problem. -A 60 room hotel is filled to capacity every night at a rate of $40 per room. The management wants to determine if a rate increase would increase their profit. They are not interested in a rate decrease. Suppose management Determines that for each $2 increase in the nightly rate, five fewer rooms will be rented. If each rented room Costs $8 a day to service, how much should the management charge per room to maximize profit?

Graph the function and locate intervals on which the function is increasing or decreasing, open intervals on which the function is concave up or concave down, and all inflection points. -

Sketch a graph of a single function that has these properties. -Find the inflection point(s) for

Provide an appropriate response. -Find vertical asymptotes for

Decide if the given value of x is a critical number for f, and if so, decide whether the point for x on f is a local minimum, local maximum, or neither. -