nesan said:Homework Statement
Consider the graph of the function f(x) = 5x^2 - 8x
Determine the average rate of change as x changes from -1 to 4
The Attempt at a Solution
f(4) - f(-1) / 4 - 1
The answer is not correct according to the answer sheet. :(
f(4) - f(-1) / 4 - 1
Average rate of change is a mathematical concept used to measure the rate at which a quantity changes over a specific period of time. It is calculated by dividing the change in the quantity by the change in time.
Average rate of change and slope are closely related concepts. In fact, average rate of change can be thought of as the slope of a line connecting two points on a graph. It measures the steepness of the line between the two points.
The main difference between average rate of change and instantaneous rate of change is the time frame over which the rate is measured. Average rate of change is calculated over a specific interval of time, while instantaneous rate of change is calculated at a specific point in time. In other words, average rate of change gives an overall rate of change over a period of time, while instantaneous rate of change gives the rate of change at a single moment.
Average rate of change is used in many real-life scenarios. For example, it can be used to calculate the average speed of a car during a road trip, the average growth rate of a plant over a month, or the average change in temperature over a day. It is also commonly used in economics and finance to measure the average rate of change in prices or stock values over a period of time.
One common misconception about average rate of change is that it is the same as the average of the starting and ending values. This is not always true, as the rate of change can vary throughout the given interval. Another misconception is that average rate of change is always constant, when in fact it can change over time. Lastly, it is important to note that average rate of change is not the same as total change, as it only considers the change in a specific quantity over time rather than the overall change.