Final answer:
The correct way to find local maxima and minima is to set the derivative of the function to zero and solve for x, then evaluate the function at the critical points to establish their nature.
Step-by-step explanation:
To find local maximum and minimum points of a function, the correct answer is:
a) Set the derivative equal to zero and solve for x. This process involves finding the critical points where the function's slope is zero, which indicate potential local maxima or minima. Additionally, you should:
c) Evaluate the function at critical points. Once you've found the critical points, you determine if they are maximum, minimum, or neither by analyzing the function's value at those points or by using the second derivative test.
Setting the function equal to zero (option b) would find the function's roots, not the local extrema. Evaluating whether the sum of the momenta in the x and y directions equates to zero (from the provided miscellaneous information) is not pertinent to finding local extrema of a function. Also, the statements regarding kinetic and potential energy (from miscellaneous information) are contextually irrelevant to the question.