Day 6 examples
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The document discusses identifying critical points, inflection points, and points of concavity for a function based on its graph over the domain [0,10]. Critical points are where the derivative is zero or undefined. Inflection points occur where the concavity changes from upward to downward or vice versa. To find inflection points, locate where the second derivative is zero or undefined and check that the second derivative has opposite signs on either side.
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![The graph of a function ƒ with domain [0, 10] is shown in the figure.
Several points are labeled.
(b) List all critical points of ƒ.](https://image.slidesharecdn.com/day6examples-120918125525-phpapp01/85/Day-6-examples-2-320.jpg)
![The graph of a function ƒ with domain [0, 10] is shown in the figure.
Several points are labeled.
(c) List all labeled points at which](https://image.slidesharecdn.com/day6examples-120918125525-phpapp01/85/Day-6-examples-6-320.jpg)
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Day 6 examples
- 2. The graph of a function ƒ with domain [0, 10] is shown in the figure. Several points are labeled. (b) List all critical points of ƒ.
- 3. The Second Derivative h→0 2 2
- 4. When tangent slopes are increasing the graph of f is concave up When tangent slopes are decreasing the graph of f is concave down f ' is increasing f ' is decreasing Inflection point Inflection point = where the direction of concavity changes Note: Sign of f '' changes at this point To find inflection points find where f'' is zero or undefined. HOWEVER, not all points will be inflection points. Must check that f'' as opposite signs on either side of point.
- 6. The graph of a function ƒ with domain [0, 10] is shown in the figure. Several points are labeled. (c) List all labeled points at which