Posted by **Anonymous** on Friday, February 4, 2011 at 12:38pm.

Let f be defined as follows.

y = f(x) = x^2 - 4 x

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

from x = 5 to x = 6

from x = 5 to x = 5.5

from x = 5 to x = 5.1

(b) Find the (instantaneous) rate of change of y at x = 5.

4

- math -
**MathMate**, Friday, February 4, 2011 at 3:11pm
(a)

Average rate of change of f(x) on an interval I = [x1,x2] equals (f(x2)-f(x1))/(x2-x1) where x2≠x1.

So if f(x)=x^2 - 4 x,

average rate of change between 5 and 6

= (f(6)-f(5))/(6-2)

= (12-5)/(6-5)

= 7

(b)

Instantaneous rate of change at x=5

=f'(5)

where

f'(x)=2x-4

so

f'(5)=10-4=6

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