Here is a piecewise polynomial function:(adsbygoogle = window.adsbygoogle || []).push({});

f(x) = x^2 + 1 if x <= 1

f(x) = 2x if x > 1

I need to prove that this function is differentiable at x = 1?

It's a parabola that turns into a line. It doesn't have any gaps or corners. The limit of f(x) as x approaches 1 is 2, and the limit of f'(x) as x approaches 1 is 2.

This was a problem on a test, but my calculus teacher took points off because she says that the function is not differentiable at x = 1.

Thanks in advance!

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# Continuously Differentiable Piecewise Function?

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