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Unformatted text preview: the average rate of change in marginal profit over the interval x = [20, 40] Solution: The average rate of change x = 2 Solution: You can apply the quotient rule to find the derivative: f ' ( x) = 5x(x − 6) (x − 3)2 x = 2 = −40 or using the definition of the limit to find the slope 3 f ( x ) − f (a ) x 2 − (−1)2 x 2 − 1
m = lim
=
=
x →a
x−a
x +1
x +1
( x + 1) ( x − 1) = ( x − 1)
=
( x + 1)
x→−1 y + 1 = (x − 1) b. c. f ( x ) = x at P = (−1, 1) Solution: = lim ( x − 1) = −2 Using the point slope form with (x, y ) = (1, − 1) y + 20 = −40( x − 2) 2 can also find the slope at x = 1 by using limit. 5 ( x + 6)
= −40
( x − 3) m = −40 23 6. Find equation of the tangent line of the following functions at t...
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This document was uploaded on 02/27/2014 for the course M 408c at University of Texas at Austin.
 Winter '06
 McAdam
 Derivative, Differential Calculus

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