Section_2.3-Getting Information from the Graph of a Function

Section_2.3-Getting Information from the Graph of a...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Section 2.3 Getting Information from the Graph of a Function Increasing and Decreasing Functions DEFINITION: A function f is called increasing on an interval I if f ( x 1 ) < f ( x 2 ) whenever x 1 < x 2 in I It is called decreasing on an I if f ( x 1 ) > f ( x 2 ) whenever x 1 < x 2 in I EXAMPLES: 1. The function f ( x ) = x 2 is decreasing on ( -∞ , 0) and increasing on (0 , ) . 2. The function f ( x ) = x 3 is increasing everywhere, that is on ( -∞ , ) . 3. The function f ( x ) = 1 x is decreasing on ( -∞ , 0) and on (0 , ) . 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Local Maximum and Minimum Values of a Function DEFINITION: A function f has a local maximum (or relative maximum ) at c if f ( c ) f ( x ) when x is near c. [This means that f ( c ) f ( x ) for all x in some open interval containing c. ] Similarly, f has a local minimum at c if f ( c ) f ( x ) when x is near c. EXAMPLES: 1. The function f ( x ) = x 2 has the local minimum at x = 0 and has no local maximum.
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2. The function f ( x ) = x 2 , x ∈ (-∞ , 0) ∪ (0 , ∞ ) has no local minimum or maximum. 3. The functions f ( x ) = x, x 3 , x 5 have no local minimum or maximum. 4. The functions f ( x ) = sin x, cos x, sec x, csc x have infinitely many local minimums and maximums. The functions f ( x ) = tan x, cot x have no local minimums or maximums. 5. The function f ( x ) = x 4 + x 3-11 x 2-9 x + 18 = ( x-3)( x-1)( x + 2)( x + 3) has two local minimums at x ≈ -2 . 6 and x ≈ 2 . 2 and a local maximum at x ≈ -. 4 . 6. The function f ( x ) = 1 has a local minimum and maximum at any point on the number line. 2...
View Full Document

{[ snackBarMessage ]}

Page1 / 2

Section_2.3-Getting Information from the Graph of a...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online