To find a function with a relative minimum at x = 1 and a relative maximum at x = 4, we can start by considering a cubic function. Let's say f(x) = (x - 1)(x - 4)(x - k), where k is a constant. To ensure that the function has a relative minimum at x = 1, the factor (x - 1) should be squared, and to ensure a relative maximum at x = 4, the factor (x - 4) should be squared. Therefore, the function can be written as f(x) = a(x - 1)^2(x - 4)^2, where a is a constant that determines the steepness of the parabola. This function will have a relative minimum at x = 1 and a relative maximum at x = 4. The constant "a" will determine the exact shape and scale of the graph.Answer:
Step-by-step explanation:
