Derivative by Definition – A polynomial function inside an absolute value – Exercise 1215

Exercise

Find by definition the derivative of the function

f(x)=|x^2-4x|

Final Answer


f&apos;(x) = \begin{cases} 2x-4, &\quad x< 0 \\ 4-2x, &\quad 0<x<4\\ 2x-4, &\quad x> 4\end{cases}

Solution

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