Posted by zoe on Sunday, November 27, 2011 at 8:36pm.
i'm not sure how to do this. can someone help, please? thanks!
consider the function f(x0 = x^2 + 2x on the interval [2, 2]
a. draw a sketch of the graph of f(x). find the average rate of change on the interval [2, 2] and sketch this secant line.
b. find an expression that calculates the instantaneous rate of change of f(x) at any given point on the curve. find the coordinates on the graph of f(x) where the instantaneous rate of change equals the average rate of change.
c. write an equation for the tangent line at the point found in part b. sketch the tangent line on the same graph as part a. what is the relationship between the two lines on the graph?
thanks for the help in advance, i'm just really confused.

calculus  michael, Sunday, November 27, 2011 at 10:43pm
a.)Sorry but I cant post the link to the graph so you gotta do that part with a calculator
To find average rate of change you need your two points with the given X values [2,2]. Those points end up being (2,0) and (2,8). Find the slope:
(80)/(2(2))=8/4=2
b.) Take derivative of your equation:
f'=2x+2
Since you wanna know where instantaneous rate of change and average rate of change are equal, set your derivative equal to your avg.:
2=2x+2
x=0
Plug your new x value into the original equation to get your coordinates (0,0)
c.)y=2x
They should be parallel.
p.s. I don't know if you need this, but the eqn. of your secant line is y=2x+4