# 4.4.7-eg - Example Consider the curve y = f x where f x =...

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

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

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

Unformatted text preview: Example Consider the curve y = f ( x ), where f ( x ) = sin(2 x- π ) , for x ∈ [- π/ 8 , 2 π/ 3] . Find the intervals where f ( x ) > 0 and f ( x ) < 0, and where f has relative (local) extrema. Also find the intervals where f 00 ( x ) > 0 and f 00 ( x ) < 0, and where f has point(s) of inflection. Then find the y-intercept of the curve, any vertical asymptotes, and the y-coordinates associated with locations of local extrema, point(s) of inflection, and endpoints. Use this information to find the absolute max/min of the function on the given interval, and to sketch the graph of the curve. Solution: The critical points of f ( x ) = sin(2 x- π ) are those x-values for which f ( x ) = 0 or f ( x ) is undefined (which does not happen for this function). Then f ( x ) = 2 cos(2 x- π ) so that f ( x ) = 0 at 2 x- π = ... ,- 3 π 2 ,- π 2 , π 2 , 3 π 2 , ..., 2 x = ... ,- π 2 , π 2 , 3 π 2 , 5 π 2 , ..., x = ... ,- π 4 , π 4 , 3 π 4 , 5 π 4 , ... ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

4.4.7-eg - Example Consider the curve y = f x where f x =...

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

View Full Document
Ask a homework question - tutors are online