5 x 6 40 x 3 m 40 23 6 find

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This document was uploaded on 02/27/2014 for the course M 408c at University of Texas at Austin.

Ask a homework question - tutors are online