Let f be defined as follows. y = f(x) = x2 − 2x (a) Find the average rate of change of y with respect to x in the following intervals.

Question

(a) Find the average rate of change of y with respect to x in the following intervals. 

from x = 6 to x = 7
from x = 6 to x = 6.5
from x = 6 to x = 6.1

(b) Find the (instantaneous) rate of change of y at x = 6. 

Answer 1

f(x) = x² - 2x

Average rate of change from x = 6 to x = 7:

[f(7) - f(6)] / (7 - 6) = [35 - 24] / 1 = 11

Instantaneous rate of change when x = 6: f'(6) = 2(6) - 2 = 10