Problem Set 04s

X 2 f 2 y 20 so we have x y 2 20

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: Set 04 Solution 2.7 Derivative as a rate of change 2.8 Derivative as a function 5x 2 − 20 5 x 2 + 20 x − 3 f ( x ) − f (a ) x − 3 () m = lim = = x →a x−a x−2 ( x − 2) ( x − 3) lim f ( x ) − f (a ) 3x − 3 3x + 3 = x x →1 x−a x −1 3x + 3 3x − 3 3( x − 1) = = ( x − 1) 3x + 3 ( x − 1) 3x + 3 m= ( = m= ) ( ) = 3 ( 3x + 3 lim x →1 ) ( 3x + 3 x→2 ) = 3 We need to find the point (x, y ) in order to use the point slope form. x = 2 ⇒ f (2) = y = −20 , so we have (x, y ) = (2 − 20 ) 3 a. f ( x ) = x − 2 x at P = (1, −1) Solution: You can use the power rule to differentiate the derivative: slope = f ' ( x) = 3 x 2 − 2 x =1 = 1 . You € 3 f (a + h ) − f (a ) (1 + h) − 2 (1 + h) + 1 m = lim = lim h→0 h→0 h h 2 (1 + 2 h + h ) (1 + h ) − 2 − 2 h + 1 = h h 3 + 3h 2 + h = lim = h 2 + 3h + 1 h→0 h m =1 f (x) = 5x 2 x −3 m = −2 7. The marginal profits of a company (in $/piece) can be described by the function: 2 at y = −0.01(x − 50) + 20 , where x is the number of pieces, and y is the marginal profit. a. Find...
View Full Document

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

Ask a homework question - tutors are online