What are the points of inflection, if any, of #f(x) = x^4/12 - 2x^2 + 15 #?
The function
Analyze the function's second derivative:
Based on the formula:
Now think about the disparity:
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There are two non-stationary points of inflection which occur at
We have:
Next, the first derivative is as follows:
The second derivative is thus as follows:
We seek out the coordinates where the second derivative vanishes, or inflection points:
When the first derivative vanishes at a point, it is considered a stationary point of inflection; if not, it is considered a non-stationary point of inflection.
Examining the function's graphs in relation to the first and second derivatives can be fascinating:
x^4/12-2x^2+15 [-6, 6, -10, 18]} graph
graph{x^3/3-4x [-10, 18, 6, -10]}
graph{x^2-4 [-10, 18, 6, 6, -10]}
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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- Please help me with this calculus applications question?

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