I need to find the lateral derivates when $x=2$ of $f:\mathbb{R}->\mathbb{R},f(x)=x^2-3$ when $x<2$ and $f(x)=10-3x$ when $x\geq 2$. I derivate them and I got that left is 4 and right is -3. But I tried to do it with this formula $\lim_{x->2,x<2,x>2}\frac{f(x)-f(2)}{x-2}$ and I do not get the same results. I get $\infty$ and $-\infty$. Am I doing something wrong?
Find the lateral derivates of the following function
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$\begingroup$
derivatives
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0Everything you said is wrong: L'Hospital does not apply here, the limits are not infinite ... – 2017-02-14
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0Ok maybe it is not l'hopital. But I learnt that you can calculate the derivate with that formula and it works cause I tried. But I do not know why I do not get this one. And I know it is not infinite because I know that they must be 4 and -3 but I can not find the mistake. – 2017-02-14
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0Just do derivative of both functions,then combine them when $x<2$ and when $x>2$ then look for the limit. – 2017-02-14