Difference between revisions of "Math 22 Concavity and the Second-Derivative Test"
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(Created page with "==Formal Definition of Concavity== Let <math>f</math> be differentiable on an open interval <math>I</math>. The graph of <math>f</math> is 1. Concave upward on <math>I</ma...") |
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2. Concave downward on <math>I</math> when <math>f'(x)</math> is decreasing on the interval. | 2. Concave downward on <math>I</math> when <math>f'(x)</math> is decreasing on the interval. | ||
| − | + | ==Test for Concavity== | |
| + | Let <math>f</math> be a function whose second derivative exists on an open interval <math>I</math> | ||
| + | 1. If <math>f''(x)>0</math> for all <math>x</math> in <math>I</math>, then the graph of <math>f</math> is concave upward on <math>I</math>. | ||
| + | 2. If <math>f''(x)<0</math> for all <math>x</math> in <math>I</math>, then the graph of <math>f</math> is concave downward on <math>I</math>. | ||
| + | |||
[[Math_22| '''Return to Topics Page''']] | [[Math_22| '''Return to Topics Page''']] | ||
'''This page were made by [[Contributors|Tri Phan]]''' | '''This page were made by [[Contributors|Tri Phan]]''' | ||
Revision as of 06:17, 31 July 2020
Formal Definition of Concavity
Let be differentiable on an open interval . The graph of is 1. Concave upward on when is increasing on the interval. 2. Concave downward on when is decreasing on the interval.
Test for Concavity
Let be a function whose second derivative exists on an open interval 1. If for all in , then the graph of is concave upward on . 2. If for all in , then the graph of is concave downward on .
This page were made by Tri Phan