Question: Show that the function f (x) = e -(1/2)[(x-)/]2 has inflection points at x = s.

Show that the function f (x) = e-(1/2)[(x-μ)/σ]2 has inflection points at x = μ ± s.

Step by Step Solution

★★★★★

3.44 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

fx e 12 fx x 2 x 1 e 1 ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Applied Calculus Questions!

Q:

The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...

Q:

Show that the function f defined by f (x) := x = x/x2 + 1; x R, is a bijection of R onto {y : 1

Q:

Show that the function f (x) = e -x2/2 has inflection points at x = 1.

Q:

UIZ # 3 Problems 3 1. Show that the function f ( x )=e x +2 x+1 is one-to-one. Graphing does not count as proof. (Hint: Use the derivative of the function.) 2. Find a formula for the inverse function...

Q:

3 Consider the function f x e 1 2 2 2 Show that x 0 is a zero of f What is the multiplicity Implement the modified Newton s method to calculate the root with tolerance 10 10 Now use the usual Newton...

Q:

( Exercise ) Score: 25 Marks 18. Find the vertical asymptote of the rational function f (x) - x 12 2x-10 2 M 18, 19. Find the horizontal asymptote of the rational function f(x) = 6x-12 2x-10 19. 2M...

Q:

( Exercise ) Score: 25 Marks 18. Find the vertical asymptote of the rational function f (x) - x 12 2x-10 2 M 18, 19. Find the horizontal asymptote of the rational function f(x) = 6x-12 2x-10 19. 2M...

Q:

We would like to use the fixed point method to find the root of the function f x e 2x is 2 and we set g x f x x What is the where 1 x 2 Suppose the initial value g x at the end of two iterations O 1...

Q:

1. (12 Pts) Find S (4x5 - 5 + ex) dx 2. (8 Pts) Find the open intervals where the function below is a) Increasing b) Decreasing 3. (12 Pts) Find J (3x2 + 2 + (x) dx 4. (24 Pts: 4 pts each) For the...

Q:

\fsh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m Math 280 Strategies of Proof Fall 2007 Class Notes 3.6 Proving Conditional Statements II: Indirect Proofs In Section 3.4, we studied...

Q:

In a particular area of the Northeast, an estimated 75% of the homes use heating oil as the principal heating fuel during the winter. A random telephone survey of 150 homes is taken in an attempt to...

Q:

McAdams Inc. uses a job-order costing system in which any underapplied or overapplied overhead is closed to cost of goods sold at the end of the month. In April, the company completed job C21F that...

Q:

Question 9 9 . If the quantity of x decreases by 6 % when the price of g d x increases by 4 % . The elasticity equals 0 . 6 6 - 0 . 6 6 1 . 5 - 1 . 5

Q:

Planning: Analyzing the Situation; Media Skills: Electronic Presentations [LO-2] Go to the PepsiCo website, at www.pepsico.com , and locate the latest annual report. Read the annual reports letter to...

Q:

One can interpret r = 0.30 as a. A weak, positive association b. 30% of the time y = y c. y changes 0.30 units for every one-unit increase in x d. A stronger association than two variables with r =...

Q:

Which one of the following statements is correct? a. The correlation is always the same as the slope of the regression line. b. The mean of the residuals from the least-squares regression line is 0...

Q:

You can summarize the data for two categorical variables x and y by a. drawing a scatter plot of the x- and y-values. b. constructing a contingency table for the x- and y-values. c. calculating the...

Q:

pls help Verde Company praduces wheels for blcycles. During the year, 661,000 wheels were produced. The actual labor used was 360,000 hours at $9.00 per hour. Verde has the following labor standards:...

Q:

For each ratio, select the building block of financial statement analysis to which it best relates. For each ratio, select the building block of financial statement analysis to which it best relates....

Q:

At December 31, Hawke Company reports the following results for its calendar year. Cash sales Credit sales $1,216,500 $2,866,000 In addition, its unadjusted trial balance includes the following items...