How to minimize given functional I confronted the next problem: we have certain values $\psi_1, \psi_2, \psi_3$ in 3 points $x_1, x_2, x_3$, also we have a general functtion with 2 undefined coefficients ($A,x_0$): $$\psi=A\exp(x-x_0)$$ We need to find this coefficients using the next functional: $$\Phi = (\psi(x_1)-\psi_1)^2+(\psi(x_2)-\psi_2)^2+(\psi(x_3)-\psi_3)^2)$$
The main goal is to compose the $\psi$ function which would be the best approximization for the given 3 values. 
As I undestand for finding $\psi(x_1), \psi(x_2), \psi (x_3)$ we need to minimize the functional $\Phi$. Can you provide us the best approach for such minimization or some other way for finding the coefficients of general function $\psi$. The photo with illustration is attached.


So you have $\Phi(x_0, A)$, it is a smooth function and you need to find its minimum. Which methods do you know that would help you to do that? For example, taking derivative and equating it to zero?
