Final answer:
The correct answer is d) Critical points are not applicable to these expressions, as the expressions provided are linear and do not have the features (like maxima or minima) associated with critical points.
Step-by-step explanation:
Critical points in mathematics often refer to particular points on a graph that represent some feature of a function, such as local maxima, local minima, or points of inflection. However, in the context of the expressions provided by the student (x - 2 - 20 or 5(10 + x) - 20), critical points in the usual sense do not apply since these are linear expressions and do not represent functions whose derivatives we would examine for maxima, minima, or points of inflection. Therefore, the correct answer is:
- d) Critical points are not applicable to these expressions.
If we were dealing with a quadratic equation of the form ax²+bx+c = 0, then we could find its roots using the quadratic formula. Those roots can be considered critical points if the quadratic is part of a function's formula, as they can indicate where the function may change direction. For example, with an equation like x² + 1.2 x 10⁻²x - 6.0 × 10⁻³ = 0, you would use the quadratic formula to find the roots or solutions, which can be critical points if we are analyzing a graph.