When asked to determine the rate of change from the first point to the second point - `x_(2) = 3 and x_(2) = 4` for the function, `y = 2^x` , will we perform the same operation as usual? Note how we have two points "considered" the same, but have different values (`x_(2) and x_(2), 3 and 4` ).
Would the following solution to this be incorrect?
Average rate = `[f(x_(2)) - f(x_(2))]/(x_(2)-x_(2)) = (16 - 8)/(4-3) = (8/1) = 8`
I suspect strongly that your problem set has a typographical error. First, there is no rate of change moving from a point to itself. Second, a function cannot have two different output values for the same input value.
Considering the problem as determine the rate of change from `x_1=3` to `x_2=4` we would get:
Yes I figured it must be a typo; however, I just wanted to receive clarification in order to be certain of my assumption. Thank you.