Final answer:
You are asked to find the change in y (dy) for a cubic function at a certain x-value and a given change in x (Δx), usually by using the derivative dy/dx; however, the Δx provided in your question is in an atypical format.
Step-by-step explanation:
The question asks to find the change in y, or dy, for a given cubic function when x is known, and a change in x, or Δx, is given by a specific expression. The function is y = x³ - 5x² + 7, and the value of x provided is 1. To solve this problem, we need to calculate the value of y at x and at x + Δx, and then find the difference between these two values to obtain dy.
However, the expression for Δx provided in the question (Δx = -0.53x² - 10x + 7 / (x + 4)) is not necessary since Δx is usually a given small increment or decrement in the value of x, rather than an expression to be evaluated. Typically, the student would use the derivative of the function y with respect to x, which can be done by finding dy/dx, and then applying it to the given x and Δx.