What is the minimum of the function $[0,1]\to[0,\infty), \lambda \mapsto e^{-aλ^2}+e^{-b(1-λ)^2}$, where $a>b>1$

Question

Doing some estimates in machine learning, I stumbled into minimizing the following function: $$f :[0,1]\to[0,\infty), \lambda \mapsto e^{-aλ^2}+e^{-b(1-λ)^2},$$ where $a>b>1$. However, imposing the derivative equal to zero, finding in this way the minimizing point and then substituting the point into the function, seems not to work well since it is not clear how to find an explicit formula for $\lambda$ such that $f'(\lambda)=0$. Any other ideas how to find an elementary expression for the minimum value of this function?