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Struggling with this for some reason. I know that you have to check for continuity but I am confusing myself.

Find the values of a and b so that the following function is differentiable in $\mathbb{R}$. $$ f(x) = \begin{cases} -3x+a, & x\ne2 \\ b, & x=2 \end{cases}$$

Thanks in advance.

MathsRookie
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  • Differentiability is more than continuity. Also, if you are confusing yourself, and would like some help, it probably helps to say what you exactly is confusing you. – B. Pasternak May 06 '18 at 18:22
  • What would you say if you were aiming for continuity? – Henry May 06 '18 at 18:29

2 Answers2

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Use that $$f'(x_0)=\lim_{h\to 0}\frac{f(x_0+h)-f(x_0)}{h}$$ if this Limit exists and $h\neq 0$

Dr. Sonnhard Graubner
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For the sake of continuity we have $b=a-6$. In that case $f(x)=-3x+a$ for all real numbers $x$ and everywhere differentiable.

Michael Hoppe
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