13112an4.4-7

# 13112an4.4-7 - c Kendra Kilmer Section 4.3 Derivatives and...

This preview shows pages 1–3. Sign up to view the full content.

c c Kendra Kilmer February 28, 2012 Section 4.3 - Derivatives and the Shapes of Curves Increasing/Decreasing Test: If f ( x ) > 0 on an interval, then f is on that interval. If f ( x ) < 0 on an interval, then f is on that interval. The First Derivative Test Suppose that x = c is a critical number of a continuous function f . 1. If f ( x ) changes from to at x = c , then we have that f ( x ) is and at x = c there is a . 2. If f ( x ) changes from to at x = c , then we have that f ( x ) is and at x = c there is a . 3. If the sign of f ( x ) is the same on both sides of x = c , then at x = c . Example 1: Determine the intervals where the following functions are increasing and decreasing and find the local extrema. a) f ( x ) = ( x + 2 ) e x b) g ( x ) = x 4 + 2 x 3 + 5 c) h ( x ) = x + 3 5 x 4

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

View Full Document
c c Kendra Kilmer February 28, 2012 Second Derivative Test for Local Extrema: Let c be a critical value for f ( x ) .
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

13112an4.4-7 - c Kendra Kilmer Section 4.3 Derivatives and...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online