(Solved): The graph of the function \( f(x)=3 x^{3}-36 x \) has one local maximum and one local minimum po ...

The graph of the function \( f(x)=3 x^{3}-36 x \) has one local maximum and one local minimum point. Find these points using the first derivative test. The function has a local maximum at the point (Type an ordered pair.) The function has a local minimum at the point (Type an ordered pair.) Determine whether the following function is continuous and/or differentiable at \( x=3 \). \[ f(x)=\left\{\begin{array}{rr} x-3 & 0 \leq x<3 \\ 8 & x=3 \\ 3 x-9 & x>3 \end{array}\right. \] Is \( f(x) \) continuous at \( x=3 ? \) A. No, because \( \lim _{x \rightarrow 3} f(x) \) does not exist. B. No, because \( \lim _{x \rightarrow 3} f(x) \) exists, but \( \lim _{x \rightarrow 3} f(x) \neq f(c) \). C. Yes, because \( f(x) \) is defined at \( x=c \) and \( \lim _{x \rightarrow 3} f(x) \) exists such that \( \lim _{x \rightarrow 3} f(x)=f(c) \). D. No, because \( f(x) \) is not defined at \( x=c \). The function \( f(x) \quad \) differentiable at \( x=3 \) because there