Question

Compute y/x for the interval [5,7], where y=5x-6.

(Use decimal notation. Give your answer to three decimal places.)



What is the instantaneous rate of change of y with respect to x at x=5?

Rate= ?

Answer 1

y = 5x - 6
when x = 5, y = 5*5 - 6 = 25 - 6 = 19
when x = 7, y = 5*7 - 6 = 35 - 6 = 29

Average rate of change over the interval [5,7] = { f(7) - f(5) } / (7 - 5) =
(29-19) / 2 = 10 / 2 = 5

What is the instantaneous rate of change of y with respect to x at x=5?
The instantaneous rate of change is the slope of the line which is the same for all values of x. Instantaneous rate = 5.