Consider the following statements:I. The derivative, where the function attains maxima or minima, is zero.II. If a function is differentiable at a point, then it must be continuous at that point.Which of the above statement(s) is/are correct?

Statement I: According to Fermat's Theorem, if a function has a local extremum (maxima or minima) at a point and the derivative exists there, then the derivative must be zero ($f^{\prime }(x)=0$). Note: This assumes the point is not a boundary point and the function is differentiable there.Statement II: It is a fundamental theorem in calculus that differentiability implies continuity. If ${\lim }_{h\to 0}\frac{f(x+h)-f(x)}{h}$ exists, then ${\lim }_{h\to 0}(f(x+h)-f(x))=0$, which proves continuity.Both statements are correct.