Determine the value of the constant k which best approximates a specified function f(x) on the interval 𝑎≤𝑥≤𝑏. Use as a cost function to be minimized:

Verify that a minimum is achieved by checking the 2nd order optimality condition.

I rewrote L(k) and then tried to find the value of k such that dL(k)/dk = 0. Am I allowed to simplify like this?