Computing an instantaneous rate of change of any function In other words, we want to look at limx→aΔfΔx=limx→af(x)−f(a)x−a. This is the slope of the line tangent to y=f(x) at the point (a,f(a)). It can also be written as a limit limh→0f(a+h)−f(a)h, where h is just another name for x−a.

You can find the instantaneous rate of change of a function at a point by finding the derivative of that function and plugging in the x -value of the point.

The average rate of change gives the slope of a secant line, but the instantaneous rate of change (the derivative) gives the slope of a tangent line. Also note that the average rate of change approximates the instantaneous rate of change over very short intervals.

The average rate is the change in concentration over a selected period of time. It depends on when you take the measurements. The instantaneous rate is the rate at a particular time. It is determined by finding the slope of the tangent to the concentration vs time curve at that time.

Understanding Rate of Change (ROC) The calculation for ROC is simple in that it takes the current value of a stock or index and divides it by the value from an earlier period. Subtract one and multiply the resulting number by 100 to give it a percentage representation.

The slope equals the rise divided by the run: . This simple equation is called the slope formula. The instantaneous rate of change, or derivative, can be written as dy/dx, and it is a function that tells you the instantaneous rate of change at any point.

Stratovolcano

A shield volcano is characterized by gentle upper slopes (about 5o) and somewhat steeper lower slopes (about 10o).

Vulcanian eruptions

One of the simplest ways to classify volcanoes is by their recent eruptive history and potential for future eruptions. For this, scientists use the terms “active,” “dormant,” and “extinct.” Determining whether a volcano is active, dormant, or extinct isn’t easy, and volcanologists don’t always get it right.