concavity and inflection points the second derivative will show where a function is concave up or...
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Concavity and Inflection Points
The second derivative will show where a function is concave up or concave down. It is also used to locate inflection points.
Concavity and Inflection Points
The second derivative will show where a function is concave up or concave down. It is also used to locate inflection points.
Concave up – this occurs as the slope of the tangent line increases
Concavity and Inflection Points
The second derivative will show where a function is concave up or concave down. It is also used to locate inflection points.
Concave up – this occurs as the slope of the tangent line increases
- As you can see, as I move from LEFT to RIGHT, the tangent line goes from a ( - ) value to a ( + ) value…
Concavity and Inflection Points
The second derivative will show where a function is concave up or concave down. It is also used to locate inflection points.
Concave up – this occurs as the slope of the tangent line increases
- As you can see, as I move from LEFT to RIGHT, the tangent line goes from a ( - ) value to a ( + ) value…
Concave down – this occurs as the slope of the tangent line decreases
- As you can see, as I move from LEFT to RIGHT, the tangent line goes from a ( + ) value to a ( - ) value…
Concavity and Inflection Points
The second derivative will show where a function is concave up or concave down. It is also used to locate inflection points.
Concave up – this occurs as the slope of the tangent line increases
Concave down – this occurs as the slope of the tangent line decreases
Concavity and Inflection Points
The second derivative will show where a function is concave up or concave down. It is also used to locate inflection points.
Concave up – this occurs as the slope of the tangent line increases
Concave down – this occurs as the slope of the tangent line decreases
Concavity and Inflection Points
The second derivative will show where a function is concave up or concave down. It is also used to locate inflection points.
Inflection Point – occur where a graph changes from concave up to concave down, or vice versa
Concavity and Inflection Points
The second derivative will show where a function is concave up or concave down. It is also used to locate inflection points.
Inflection Point – occur where a graph changes from concave up to concave down, or vice versa
Concavity and Inflection Points
The second derivative will show where a function is concave up or concave down. It is also used to locate inflection points.
Inflection Point – will occur where a graph changes from concave up to concave down, or vice versa
Inflection point
Concavity and Inflection Points
Concavity and Inflection Points
Concavity and Inflection Points
Concavity and Inflection Points
2. Set up your intervals
0 1
Concavity and Inflection Points
2. Set up your intervals
0 1
Concavity and Inflection Points
2. Set up your intervals
Concavity and Inflection Points
2. Set up your intervals
- place on number line
Concavity and Inflection Points
2. Set up your intervals
Concavity and Inflection Points
2. Set up your intervals Concave up
CU
Concavity and Inflection Points
2. Set up your intervals Concave up
CU
Concave up
CU
Concavity and Inflection Points
2. Set up your intervals Concave up
CU
Concave up
CU
Concave down
CD
Concavity and Inflection Points
2. Set up your intervals Concave up
CU
Concave up
CU
Concave down
CD
Concave down
CD
Concavity and Inflection Points
Concavity and Inflection Points
Concavity and Inflection Points
2. Set up your intervals
Concavity and Inflection Points
2. Set up your intervals
Concavity and Inflection Points
2. Set up your intervals
- place on number line
** yes, it is possible that a critical point will also be an inflection point
Concavity and Inflection Points
2. Set up your intervals
Concavity and Inflection Points
2. Set up your intervals
CU
Concave up
Concavity and Inflection Points
2. Set up your intervals
CU
Concave up
Concave down
CD
Concavity and Inflection Points
2. Set up your intervals
CU
Concave up
Concave down
CD
Concave up
CU
Concavity and Inflection Points
2. Set up your intervals
CU
Concave up
Concave down
CD
Concave up
CU
Concave up
CU