How do you find a, b, and show that that 𝑓(𝑥) has a local min value?

[angela107]

Homework Statement

Will my local minimum be x=1?

Relevant Equations

n/a

 

[BvU]

Homework Statement:: Will my local minimum be x=1?

You get a whole story but you don't believe the happy end ? What is your real question / doubt ?

 

[RPinPA]

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?

 

[angela107]

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?

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 $x=1$.

 

[angela107]

You get a whole story but you don't believe the happy end ? What is your real question / doubt ?

I've checked my work, but can you double-check?