2.2 day 2 presentation.notebook
October 15, 2012
a) Find an equation of the tangent line to the graph of f at the indicated point.
b) Use a graphing utility to graph the function and its tangent line at the point
c) Use the derivative feature of your calculator to confirm your results
54. y=x3+x Point:(1,2)
Oct 10­1:49 PM
Determine the point(s), (if any) at which the graph of the function has a horizontal tangent line
60. y=x2+1
Oct 5­8:44 AM
64. Find k such that the line is tangent to the graph of the function.
Line
Function
y=­4x+7
f(x)=k­x 2
Oct 5­8:50 AM
Average Rate of Change over an interval
The average rate of change of a function over an interval is simply the slope of the secant line over the interval.
The average rate of change for f(x) over [A,B] is:
Oct 5­8:52 AM
Instantaneous Rate of Change
The instantaneous rate of change of a function at x=a is simply the slope tangent line at x=a ­> f'(a)
The instantaneous rate of change for f(x) at x=a is:
f'(a)
The instantaneous rate of change for f(x) at x=b is:
f'(b)
Oct 5­1:08 PM
Oct 5­1:08 PM
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2.2 day 2 presentation.notebook
October 15, 2012
Find the average rate of change of the function over the indicated interval. Compare this average of change with the instantaneous change at the endpoints of the interval.
g(t) = 2t3 ­ 1 [0,1]
Oct 5­1:24 PM
Oct 5­2:51 PM
Oct 6­1:59 PM
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