Final answer:
To find the intervals where the graph of the function f(x) = -x⁴ + 32x³ - 32x + 11 is increasing or decreasing, one must perform calculus operations involving the first and possibly second derivatives to analyze the critical points.
Step-by-step explanation:
The student's question addresses the topic of determining the intervals in which the graph of a given polynomial function is increasing or decreasing. In this case, the function in question is f(x)=-x⁴+32x³-32x+11. To find out where the graph is increasing or decreasing, one must consider the function's derivatives and analyze its critical points. Since the provided information and excerpts do not directly relate to the function given in the question, our approach will involve calculus, specifically finding the first derivative of the function, setting it equal to zero to find the critical points, and using the second derivative or a sign chart to determine concavity and the nature of these critical points. This will allow us to describe the intervals where the function is increasing or decreasing.