tangent(2)N.notebook
September 21, 2011
Find the average rate of change of the function f(x) = x2 + 2x + 1 over the interval [1,4]. What does this number represent?
Slope of the Tangent Line
Slope of the Curve at x = a.
provided the limit exists
*This is a difference quotient*
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tangent(2)N.notebook
ex. f(x) = x2 ­ 2x
a) Find the slope of the curve at x = a.
September 21, 2011
c) When is there a horizontal tangent?
What is the slope of a horizontal tangent?
b) Find the slope at a = 2? a = 4?
What is happening?
Instantaneous Rate of Change = speed = slope of tangent =slope of curve
d) Find the equation of the normal line.
The normal line is perpendicular to the tangent line
ex. Suppose a rocket accelerates from rest under
the condition s = 10t2 where s is the # of feet
the rocket travels in t seconds. Find the
speed at time t = 3
6 ft/sec
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tangent(2)N.notebook
September 21, 2011
Does the tangent line exist?
The slope must approach the same value from the left and the right!!!
=
ex. f(x) =
Journal: Explain how the slope of the tangent line is found. How does the average rate of change help find this?
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tangent(2)N.notebook
September 21, 2011
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