# A popular method for curve fitting is the “Least Squared&rdqu...

## Transcribed Text

A popular method for curve fitting is the βLeast Squaredβ method. a) Determine the value of the constant k which best approximates a specified function f(x) on the interval π β€ π₯ β€ π. Use as a cost function to be minimized: πΏ(π) = 1 2 β« [π β π(π₯)] 2ππ₯ π π Verify that a minimum is achieved by checking the 2nd order optimality condition. b) Determine the optimal value of π and πΏ(π) in fractional form for π(π₯) = π₯ 2 , π = 0, πππ π = 1. c) For the best linear fit, determine the optimal value of π, π πππ πΏ(π) in fractional form for π(π₯) = π₯ 2 , π = 0, πππ π = 1 where, πΏ(π, π) = 1 2 β« [ππ₯ + π β π(π₯)] 2ππ₯ π π Hint: The answers to these problems can be confirmed using MATLABβs or Excelβs curve fitting. In part a. we need to solve ππΏ(π) ππ = 0

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