Finding the function with two coordiantes and one f'(x) cord.

[KayVee]

Homework Statement

I'm having troubles calculating a function, because one of the given data is: $$f'(2)=1$$

The other two are f(0)=3.5 and f(5)=6.

If three "normal" coordinates are given, i.e (0 ; 3,5) (5 ; 6) and the last one was (2 ; 1), there would be no problem. But how can I transform the f'(2)=1 to a f(x)=y?

Homework Equations

If there were three normal coordinates, I would use the equation: $$f(x)=a*x^2+b*x+c$$

The Attempt at a Solution

Since this is the first time I experience the given data, I have no equations for the problem. But I tried to make a differential equation of the function and setting it to zero, but nothing helped.

P.S
I'm still not familiar with the Latex function, since this is my first (or second) homework post. But I need to learn it. Hope you can understand my problem.

 

[union68]

You were right with your assumption that the function should be of the form

$$f\left(x\right) = ax^2+bx+c$$.

What is $$f'\left(x\right)$$ then? Plug your values into f and f' and you'll have three unknowns and three linear equations.

 

[KayVee]

Thanks union68, that worked just fine