1. The similarity of the turning points and the points of inflexion is both of them can be stationary point, but not all the stationary points are turning points or points of inflexion. A turning point is a point which is the point of the sign of the derivative changes. And the turning points are the local maximum and minimum where the derivative of the function changes from positive to negative or from negative to positive. When the shape of the function is smooth, the turning point will be a stationary point.

(As shown in the graph, the points are the turning points of this graph.)

The points of inflexion are the points on the curve which is the sign of the curvature changes. The points of inflexion can be the stationary points but not the local maximum or minimum. After the first derivative, points of inflexion can be categorised to two different kinds: if f’(x) =0, this point is a stationary point of inflexion; if f’(x) ≠0, this point is a non-stationary point of inflexion. There is a condition for the points of inflexion in second derivative which is f”(x) need to equal to zero or not exist. On the both sides of the inflexion points, the graph will be increasing or decreasing on both sides.

As showing in the graph, the point (0, 0) is the inflexion point. 2. People use differential equations to predict the spread of diseases through a population. Populations usually grow in an exponential fashion at first:

However, populations do not continue to grow forever, because food, water and other resources get used up over time. Differential equations are used to predict populations of people, animals, bacteria and viruses that are being affected by external events. The logistic equation (developed in the mid-19th century) allows for a growth term AND an inhibition term. It is predicted that the AIDS epidemic will follow the pattern of the logistic equation. If

A = number of people affected by the virus at time t,
P =...

...however goods might differ not just in prices, but also in other characteristics such as variety and quality. As pointed out by Waterson (1989) and Cremer et al. (1991), “product differentiation is one of the pervasive features of modern economies” and “most of the real world markets are characterised by product differentiation”. Goods, even if they satisfy identical needs, are not always identical, homogenous. At the same time, consumers are not identical either:...

...DIFFERENTIATION STRATEGY
In this paper work we will talk about Differentiation Strategy. In contrast to the cost leadership strategy, implementation of a differentiation strategy means that value is provided to customers through the unique features and characteristics of a company's products rather than by the lowest price. Because differentiated products satisfy customers' unique needs or preferences, companies can charge premium prices for...

...Differentiation Framework
July 13, 2013
Differentiation Framework
The following paper contains a discussion of (1) Jack Welch’s differentiation framework, (2) A, B, C position categorization and (3) process that must be in place for successfully differentiating your workforce.
Jack Welch’s 20-70-10 Differentiation Framework
No other principle brings more controversy, and is more misunderstood than Jack Welch’s 20-70-10...

...Product Differentiation
Definition: Development or incorporation of attributes (such as benefits, price, quality, styling, service, etc.) that a product's intended customers perceive to be different and desirable. Advertising and promotion of a product is based on its differentiating characteristics.
Source: http://www.businessdictionary.com/definition/product-differentiation.html
Today, the market is crowded with similar brands, clamoring for the attention of customers....

...Differentiation
In this short essay I intend to explain the meaning of differentiation....
In order to fully explain differentiation it is important to turn to The National Curriculum and look at what has become known as the ‘general inclusion statement’. This statement contains a statement that defines inclusion as “a demand on teachers not to ignore the three principles of inclusion (below) in their planning” Session 1 / Inclusion, the...

...The next option is a broad differentiation strategy providing products or services that offer benefits different from those of competitors and that are widely valued by buyers. The aim is to achieve competitive advantage by offering better products or services at the same price or enhancing margins by pricing slightly higher.
Differentiation may be achieved in a number of ways. The product may incorporate a more innovative design, may be produced using advanced...

...Differentiation in the Classroom
Brittany Hunt
University of Toledo
Differentiated instruction in the classroom can be beneficially for every child’s needs to learn to their best ability. Differentiation means tailoring instruction to meet individual needs. Whether teachers differentiate content, process, products, or the learning environment, the use of ongoing assessment and flexible grouping makes this a successful approach to instruction. No student...

...Individual Assignment 2
Boost Juice utilize various differentiation variables when differentiating its products from its competitors like, Top juice, Berri, Starbucks and various others. Differentiation is distinguishing a product or service from ones competitors and Boost juice achieves differentiation through product, service, personnel, channel and image. Boost Juice faces potential macroeconomic forces that could impact Boost Juices’ from...