Determine the parameters ? and ? so that the function

[Erros]

Determine the parameters ? and ? so that the function [math]? (?) = ax-\frac{b}{x}[/math]has a minimum in point
A (1,2)
Hi I don't know how to do this task, I tried over the excerpt and
I got it

[math]a+\frac{b}{x^{2}}[/math]

But I just don't know what's next and how?

 

[Dr.Peterson]

Determine the parameters ? and ? so that the function [math]? (?) = ax-\frac{b}{x}[/math]has a minimum in point
A (1,2)
Hi I don't know how to do this task, I tried over the excerpt and
I got it

But I just don't know what's next and how?

What you've found here is the derivative, f'(x), right?

What has to be true of f(1), and of f'(1)? That will give you two equations in a and b.

 

[pka]

Determine the parameters ? and ? so that the function [math]? (?) = ax-\frac{b}{x}[/math]has a minimum in point
A (1,2)
Hi I don't know how to do this task, I tried over the excerpt and
I got it

But I just don't know what's next and how?

If you got [imath]f^{\prime}(x)=a+bx^{-2}[/imath] then what is [imath]f^{\prime\prime}(x)=~?[/imath]
Tell us why it must true that [imath]f(1)=2~?[/imath]
What must be true of [imath]f^{\prime}(1)=~?~\&~f^{\prime\prime}(1)=~?[/imath] And WHY?"
[imath][/imath][imath][/imath]

 

[Steven G]

Calculus, at least in this problem, is like a game. Before you play the game you need to know the rules. What information does the 1st and 2nd derivative tell you?

 

[JeffM]

Actually, this problem is a little tricky conceptually because we seem have three independent constraints, two strong and one weak, but only two parameters. It was not initially clear to me that the problem would necessarily be solvable. Then I realized that the weak constraint is automatically satisfied by the conditions of the problem.