I am not familiar with Lagrange multipliers. I am trying to minimize the following equation
$$\text{minimize}~ 5\sqrt{36+x^2}+4(20-x)$$ $$\text{subject to}~ 0 \leq x \leq 20$$
Can I use the Lagrange multipliers to solve this minimization problem? Is the equation $$5\sqrt{36+x^2}+4(20-x)-\lambda_1(x-20)+\lambda_2 x = 0$$ correct? I know that the answer is x=8, but I am not finding this value. Can you tell me a good reference for beginners?