Sketching - c,f ( c )) is neither a relative maximum nor a...

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

View Full Document Right Arrow Icon
Sketching the curve of y = f ( x ) 1. Find any x - and y -intercepts. x -intercept is a point where y = 0. y -intercept is a point where x = 0. For rational functions we may consider the vertical or horizontal asymptotes. x = k making the denominator zero is the vertical asymptote. y = lim x →∞ f ( x ) is the horizontal asymptote. 2. Find all critical points for y = f ( x ) that are all values of x where f 0 ( x ) = 0 or where f 0 ( x ) is undefined. 3. Knowing the critical points, determine where the function f ( x ) is increasing or decreasing. f ( x ) is increasing where f 0 ( x ) > 0. f ( x ) is decreasing where f 0 ( x ) < 0. 4. Find the relative maximum and minimum values. First Derivative Test : Let ( c,f ( c )) be a critical point. (a) If f 0 ( x ) changes from positive to negative at x = c , then the point ( c,f ( c )) is a relative maximum. (b) If f 0 ( x ) changes from negative to positive at x = c , then the point ( c,f ( c )) is a relative minimum. (c) If f 0 ( x ) does not change sign at x = c , then the point (
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: c,f ( c )) is neither a relative maximum nor a relative minimum. Second Derivative Test : Let ( c,f ( c )) be a critical point. (a) If f 00 ( c ) &amp;lt; 0, then the point ( c,f ( c )) is a relative maximum. (b) If f 00 ( c ) &amp;gt; 0, then the point ( c,f ( c )) is a relative minimum. Note that if f 00 ( c ) = 0 or if f 00 ( c ) is undened, then the test fails and the rst derivative test should be used instead. 1 2 5. Find the points of inection that are all values of x where f 00 ( x ) = 0 and f 00 changes the sign at those points. 6. Knowing the points of inection, determine where the function f ( x ) is concave up or concave down. (a) f ( x ) is concave up where f 00 ( x ) &amp;gt; 0. (b) f ( x ) is concave down where f 00 ( x ) &amp;lt; 0. 7. Sketch the curve using all information....
View Full Document

This note was uploaded on 03/17/2011 for the course PHYSICS 2001 taught by Professor Young during the Spring '08 term at LSU.

Page1 / 2

Sketching - c,f ( c )) is neither a relative maximum nor 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