Optimization Problem - Least square

A popular method for curve fitting is the “Least Squared” method.
a) 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.
b) Determine the optimal value of k and L(k) in fractional form for f(x)=x²,a=0,and b=1.
c) For the best linear fit, determine the optimal value of k,m and L(k) in fractional form for f(x)=x²,a=0,and b=1 where,
Hint: The answers to these problems can be confirmed using MATLAB’s or Excel’s curve fitting.
In part a. we need to solve dL(k)/dk=0

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