For a function f(x) the derivative at x=2 is 5. Is the derivative of f(x) continuous at x=2? Thanks!
3 answers
If a function has a derivative at a point, the function must be continuous there.
Isn't it asking if the derivative is continuous? Not whether the function is continuous?
Yes, I misread the question. My mistake.
According to this reference:
http://www.math.colostate.edu/~reinholz/ed/08fa_m160/lectures/mean_value_theorem.pdf
the existence of a derivative of a function at a point does not necessarily imply that the derivative is continuous. An example is provided of a function with derivatves throughout a region for which the derivative is not continuous at one point in the region.
According to this reference:
http://www.math.colostate.edu/~reinholz/ed/08fa_m160/lectures/mean_value_theorem.pdf
the existence of a derivative of a function at a point does not necessarily imply that the derivative is continuous. An example is provided of a function with derivatves throughout a region for which the derivative is not continuous at one point in the region.
1 answer