Saturday

December 20, 2014

December 20, 2014

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

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

**Answer this Question**

**Related Questions**

math - Let f be defined as follows. y=f(x)=x^2-12x (a) Find the average rate of ...

CALC SHOULD BE EASYISH - Let f be defined as follows. F(x)=y=x^2 -7 (a) Find the...

calculus - Let f be defined as follows. F(x)=y=x^2 -7 (a) Find the average rate ...

Calculus - Let f be defined as follows. y = f(x) = x^2 - 4 x (a) Find the ...

Math - At a temperature of 20°C, the volume V (in liters) of 1.33 g of O2 is ...

calc - Using Ohm's Law (V=IR), where units are volts, amperes, and ohms, and V ...

Calculus - y = f(x) = x^2 - 6 x (a) Find the average rate of change of y with ...

calculus - At a temperature of 20°C, the volume V (in liters) of 1.33 g of O2 is...

calculus - Find the average rate of change f(x)=x^3-8x+9 a. from -3 to -2 b. ...

College Algebra - Let h(12) = -100 for some function h(x), defined everywhere. ...