A function is said to be differentiable at a number c if its derivative at x=c exists.
Question
A function is said to be differentiable at a number c if its derivative at x=c exists.
Solution
Yes, that's correct. A function is considered differentiable at a point c if the derivative of the function exists at that point. This means that the function has a non-vertical tangent line at the point (x=c), and the function is not having any kind of discontinuity or sharp turn at that point. The derivative of the function at x=c, often denoted as f'(c) or df/dx|_(x=c), gives the slope of the tangent line to the function at that point. If this derivative does not exist, then the function is not differentiable at x=c.
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