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Numerade Educator

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Problem 71 Hard Difficulty

Let.
$ f(x) = \left\{
\begin{array}{ll}
x^2 + 1 & \mbox{if} x < 1\\
x + 1 & \mbox{if} x \ge 1 \\
\end{array} \right.$
Is $ f $ differentiable at 1? Sketch the graphs of $ f $ and $ f '. $

Answer

$f$ is not differentiable at 1

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Video Transcript

So it's the F differential poet. Well, I'll leave the sketching part of you. And for the first part, if it's not differentiable one bills derivative of this part is two X and this is two at X equals one. And the reality of this is what so which is one at ethics FC Host one and they do not match. Oh, when they don't match, you don't have a a value for the the slope of the tangent line, therefore is not differentiable.