Final answer:
The question focuses on understanding a function's behavior based on its derivative. A derivative that is positive across all real numbers indicates a function that is ever-increasing over that domain. The correct understanding of slopes and function behavior at specific points is crucial in determining the function's properties.
Step-by-step explanation:
The student's question pertains to the behavior of a function and its derivative. When assessing the defined function h(z) = 2z² - 1, its derivative, h'(z) = 4z, is always positive for all real numbers, which indeed indicates that the function h(z) is increasing on the interval (-∞, ∞). So, for the function f(x) in choice 75., option b. y = x² might initially seem correct, but because its slope is not always positive (for negative values of x), we need to be careful in concluding which function exhibits a positive value with a positive, yet decreasing, slope at x = 3. Furthermore, to fully answer the question, we must evaluate each option in light of the described behavior of f(x) at the specific point given.