Sketch a qualitatively accurate picture of the graph

Reference no: EM131014271

Let f(x) = x³ - 3 a²x 4 + a³

where a is some positive constant.

a. Find f(0), f( - 2a), f(a), f(2a). Then argue that the function has 3 roots.

b. Find the intervals where f(x) is increasing and the intervals where f(x) is decreasing. Your answer will depend on a. (Hint: Treat a as a constant when you differentiate. For instance, the derivative of -3a²x is -3a².)

c. Find the intervals where f(x) is concave up and where it is concave down.

d. Sketch a qualitatively accurate picture of the graph.

Reference no: EM131014271

Questions Cloud

Find math lesson plans that concentrate : Select a grade level and from three websites find math lesson plans that concentrate on a particular math performance from the NCTM Standards for Number Sense and Operations

Use the arithmetic average : Suppose the rate of return on a 10-year T-bond is 6.85%, the expected average rate of inflation over the next 10 years is 2.0%, the MRP on a 10-year T-bond is 0.9%, no MRP is required on a TIPS, and no liquidity premium is required on any Treasury se..

Why is milk sold in rectangular containers : Discuss the economics of Franks question - Why is milk sold in rectangular containers, while soft drinks are sold in round one

Corporate tax rate-depreciation and amortization expense : Trevi Corporation recently reported an EBITDA of $32,000 and $9,700 of net income. The company has $6,600 interest expense, and the corporate tax rate is 35 percent. What was the company’s depreciation and amortization expense?

Sketch a qualitatively accurate picture of the graph : Sketch a qualitatively accurate picture of the graph. Find the intervals where f(x) is concave up and where it is concave down.

Does it appear that growth was faster in the treated plots : The researchers used a matched pairs t test to see if the data give good evidence of faster growth in the treated plots. State hypotheses, carry out the median increase in heart rate and apply the Wilcoxon signed rank test. What do you conclude?

Currently has negative earnings-benchmark price-sales ratio : TwitterMe, Inc., is a new company and currently has negative earnings. The company’s sales are $2,200,000 and there are 155,000 shares outstanding. If the benchmark price-sales ratio for the company is 4.6, how much will you pay for the stock? If the..

Challenges of posting us employees to overseas locations : Consider the challenges of posting U.S. employees to overseas locations. You will develop a 25 - 30 slide presentation to make recommendations on the HR-related challenges.

What are the critical issues to be addressed : How should a company monitor implementation to help ensure successful implementation? What use(s) should be made of monitoring results?

User Account

All Pages