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Proving Derivative Existence – A function with parameters – Exercise 1123

Exercise

Given the function (a and b parameters)

f(x) = \begin{cases} a\cdot \cos x, &\quad x\leq 0 \\ b\cdot \sin(x+c\pi), &\quad x >0\\ \end{cases}

For which values of the function parameters is it differentiable?

Final Answer


\begin{cases} a=0 \\ b=0\\ c, &\quad c\in R \end{cases}

Or

\begin{cases} a =\pm b \\ c=\frac{1}{2} +n, &\quad n\in Z\\ \end{cases}

 

Solution

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