In your own words, explain how to find the rate of change of the following graph at x=1 . Then find the rate of change at x=1 .

Answer 1

To find the rate of change at a specific point on a graph, we can look at the slope of a tangent line at that point.

First, draw a tangent line that touches the graph at the point x=1. This tangent line should pass through the point (1, f(1)), where f(x) is the equation of the graph.

Next, find two points on this tangent line that are close to the point x=1. For example, we can choose a point slightly to the left of x=1 and a point slightly to the right of x=1.

Now, calculate the difference in the y-coordinates of these two points on the tangent line, and divide it by the difference in the x-coordinates of these two points. This will give us the slope of the tangent line, which represents the rate of change at x=1.

Finally, determine the rate of change by plugging in the x-coordinate value of x=1 into the equation of the tangent line. This will give us the exact value of the rate of change at x=1.

Note: The rate of change is also known as the instantaneous rate of change or the derivative. It represents how fast the y-values of the function are changing with respect to the x-values at a specific point.

Without knowing the specific equation or shape of the graph, I am unable to find the rate of change at x=1.