## What is a turning point in history?

The dictionary defines “turning point” as a point at which a decisive change takes place. So a turning point in history is more than just an important event that happened a long time ago. It is an idea, event or action that directly, and sometimes indirectly, caused change.

## What are 5 changes brought about by the Industrial Revolution?

The technological changes included the following: (1) the use of new basic materials, chiefly iron and steel, (2) the use of new energy sources, including both fuels and motive power, such as coal, the steam engine, electricity, petroleum, and the internal-combustion engine, (3) the invention of new machines, such as …

## What is the maximum point?

Maximum, In mathematics, a point at which a function’s value is greatest. If the value is greater than or equal to all other function values, it is an absolute maximum.

## What marks the Industrial Revolution?

The Industrial Revolution was the transition to new manufacturing processes in Europe and the United States, in the period from about 1760 to sometime between 1820 and 1840. The development of trade and the rise of business were among the major causes of the Industrial Revolution.

## How did the Industrial Revolution move society forward?

The Industrial Revolution moved people away from their humanity as they dealt with unsanitary and/or unsafe living and working conditions. The Industrial Revolution moved people toward opportunity as technology made travel easier and manufacturing jobs gave rise to a middle class.

## Is the minimum point the turning point?

The turning point of a graph is where the curve in the graph turns. The turning point will always be the minimum or the maximum value of your graph.

## What happens when the first and second derivative is 0?

Since the second derivative is zero, the function is neither concave up nor concave down at x = 0. It could be still be a local maximum or a local minimum and it even could be an inflection point. Let’s test to see if it is an inflection point. We need to verify that the concavity is different on either side of x = 0.

## What’s the critical point?

In thermodynamics, a critical point (or critical state) is the end point of a phase equilibrium curve. The most prominent example is the liquid–vapor critical point, the end point of the pressure–temperature curve that designates conditions under which a liquid and its vapor can coexist.

## How do you find a point of inflection?

They can be found by considering where the second derivative changes signs. In similar to critical points in the first derivative, inflection points will occur when the second derivative is either zero or undefined.

## What is the difference between first and second derivative?

The first derivatives are used to find critical points while the second derivative is used to find possible points of inflection. By itself, a first derivative equal to 0 at a point does not tell you whether that point is actually an extrema.

## What happens when the derivative is 0?

2 Answers. The derivative of a function, f(x) being zero at a point, p means that p is a stationary point. That is, not “moving” (rate of change is 0).

## How do you prove a point is a minimum?

So, dy dx goes from negative, to zero, to positive as x increases. In other words, dy dx must be increasing as x increases. dx2 is positive at a stationary point, then that point must be a minimum turning point. dx2 > 0 there, then that point must be a minimum.

## What is the turning point?

A turning point is a specific, significant moment when something begins to change. Historians might say that Rosa Parks’s famous bus protest was a turning point in the Civil Rights Movement. Looking back at historical events, it’s fairly easy to mark various turning points.

## How do you prove maximum points?

Method 1: If f'(x)>0 for all amaximum at x=c. If f'(x)<0 for all a0 for all c