Understanding Average Rate of Change

The video tutorial explains how to find the average rate of change of a function, specifically f(x) = -x^2 + 9/x, over the interval from x=1 to x=6. It demonstrates calculating function values at these points, finding the change in outputs and inputs, and interpreting the result as a slope between two points. The tutorial concludes with a graphical representation of the function and the average rate of change.

What is the average rate of change of a function equivalent to?

• The slope of a tangent line

• The slope between two points

• The derivative of the function

• The integral of the function

What is the function value when x = 1 for the function f(x) = -x^2 + 9/x?

• 9

• 7

• 8

• 10

What is the function value when x = 6 for the function f(x) = -x^2 + 9/x?

• -72/2

• -71/2

• -70/2

• -69/2

What is the change in the function values from x = 1 to x = 6?

• -17/2

• -69/2

• -8

• -85/2

What is the change in the x-values from x = 1 to x = 6?

• 5

• 7

• 4

• 6

What is the average rate of change of the function on the interval from 1 to 6?

• -8

• -69/2

• -85/2

• -17/2

What does the numerator in the average rate of change represent?

• Sum of y-values

• Change in y-values

• Change in x-values

• Sum of x-values

What does the denominator in the average rate of change represent?

• Change in x-values

• Change in y-values

• Sum of x-values

• Sum of y-values

How does the average rate of change relate to the graph of the function?

• It is the slope of the tangent line at a point

• It is the area under the curve

• It is the slope of the secant line between two points

• It is the maximum value of the function

What does the average rate of change indicate about the function on the interval?

• The function value remains constant

• The function value decreases by 17 every time the input increases by 2

• The function value increases by 17 every time the input increases by 2

• The function value doubles