4.2.6-eg-1

# 4.2.6-eg-1 - f ( x ) = 2 x 3-x 2 + C, (2) where C is an...

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

Example 1. Find all functions which have the derivative f 0 ( x ) = 6 x 2 - 2 x. 2. Find the function f which has as its derivative f 0 ( x ) = 6 x 2 - 2 x and whose graph passes through the point (2 , 13). Solution: 1. Recalling that d dx ± x 3 ² = 3 x 2 , = d dx ± 2 x 3 ² = 6 x 2 , and d dx ± x 2 ² = 2 x, it follows that the function f ( x ) = 2 x 3 - x 2 is such that f 0 ( x ) = 6 x 2 - 2 x. (1) But there are an inﬁnite number of functions with this derivative, each diﬀering by a constant. It follows that all functions with derivative given by (1) are of the form
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: f ( x ) = 2 x 3-x 2 + C, (2) where C is an arbitrary real-valued constant. 2. From #1, we are seeking a function of the form of f ( x ) in (2) for which f (2) = 13 . That is, we need to ﬁnd C so that 2 · 2 3-2 2 + C = 13 = ⇒ C = 13-12 = 1 ....
View Full Document

## This note was uploaded on 04/02/2012 for the course MTH 132 taught by Professor Kihyunhyun during the Fall '10 term at Michigan State University.

Ask a homework question - tutors are online