Thursday 18 February 2016

Derivative of Square Root Polynomial?



How do you find the derivative of





$\sqrt{x^2 - 4x + 4}$




I applied Chain rule and got this




$\frac{x-2}{\sqrt{(x-2)^2}}$




However, the fill-in box requires two distinct functions (piecewise) where x > ______ and x < _____.




How would I get two equations from the derivative?



Problem Img


Answer



Hint: $\sqrt{x^2-4x+4}=\sqrt{(x-2)^2}=|x-2|$


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