- #1
angela107
- 35
- 2
- Homework Statement
- Will my local minimum be x=1?
- Relevant Equations
- n/a
How do you find a, b, and show that that đť‘“(đť‘Ą) has a local min value?
Click For Summary
Homework Help Overview
The discussion revolves around finding the constants a and b for the function f(x) = ax² + b/x, given that the graph has a horizontal tangent at the point (1,3). Participants are also exploring how to demonstrate that f(x) has a local minimum at x=1.
Discussion Character
- Exploratory, Assumption checking, Problem interpretation
Approaches and Questions Raised
- Participants are attempting to clarify the original question and the context of the problem, particularly regarding the conditions for the horizontal tangent and the implications for local minima. There is also a focus on verifying the correctness of the values for a and b.
Discussion Status
The discussion is ongoing, with some participants providing guidance on the correctness of the solution for a and b, while others are seeking clarification on the original question and its requirements. There is no explicit consensus yet, as participants are still exploring the details of the problem.
Contextual Notes
Participants note the importance of the information provided about the horizontal tangent and the specific point (1,3) in relation to the function's behavior. There is an emphasis on the need for clarity in the problem statement to facilitate better understanding and discussion.
- #2
BvU
Science Advisor
Homework Helper
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You get a whole story but you don't believe the happy end ? What is your real question / doubt ?angela107 said:
- #3
RPinPA
Science Advisor
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Is the attached picture your solution? You didn't tell us the question so it takes some guesswork to figure out what the question was. The attached text says "Since there is a horizontal tangent at the point (1,3)". Was that part of the question, some information you were given? And I have to assume that the form of f(x) you gave us was what you were given.
Given those two things, your solution for a and b is correct, and your conclusion about x = 1 being a local minimum is also correct.
Was that what you were asked to prove? If so, you have done so.
Could you in future please provide the question?
Given those two things, your solution for a and b is correct, and your conclusion about x = 1 being a local minimum is also correct.
Was that what you were asked to prove? If so, you have done so.
Could you in future please provide the question?
- #4
angela107
- 35
- 2
sorry, the question is "the graph of the function ##f(x)=ax^2+\frac{b}{x}## has a horizontal tangent at point (1,3). Find ##a##, ##b##, and show that ##f(x)## has a local minimum value at ##x=1##.RPinPA said:
- #5
angela107
- 35
- 2
I've checked my work, but can you double-check?BvU said:
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