calculus
Consider the function f(x) = piecewise [(x^3)(cos(1/x)) , x=/=0], [0, x=0]. Use the definition of the derivative at a point to determine if f is differentiable at x=0
I am not sure how to start this question. Am I supposed to plug in x = 0?
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Answers
Yes, you are correct. To determine if f is differentiable at x = 0, you would need to calculate the derivative of f at that point. To do this, you would need to plug in x = 0 into the definition of the derivative. The definition of the derivative states that the derivative of f at a point is the limit of the change in y (f(x)) divided by the change in x (x - 0), as x approaches 0 from either side. In this case, the denominator would always be 0, so the derivative of f at x = 0 would be undefined. Therefore, f is not differentiable at x = 0.
