To sketch this function, focus on the key features provided by the sign patterns of `f'(x`) and `f''(x)`, as well as the given points where `f(x) = 0`, `f'(x) = 0`, and `f''(x) = 0`. Start by plotting these critical points. Then, use the sign of `f'(x)` to determine where the function is increasing or decreasing, and the sign of `f''(x)` to determine the concavity. Remember that a change in the sign of `f'(x)` indicates a local extremum, while a change in the sign of `f''(x) ` indicates an inflection point.