Question

Let f be a function such that f(1)=2 . At each point (x,y) on the graph of f, the slope is given by dy/dx=5xyx2y25 . Which of the following statements is true?

A. f has a relative minimum at x=1
B. f has a relative maximum at x=1
C. F has neither a relative maximum or minimum at x=1
D. There is not enough information

Answer 1

The question concerns the behavior of a function at x=1 based on the given slope. There is a typo in the slope expression, but based on the corrected assumption, the function has a positive slope at x=1. Without more information about the slope's behavior near x=1, we cannot determine if there is a relative extreme point, hence the correct answer is D: not enough information.

Step-by-step explanation:

The question asks about the behavior of the function f at the point where x=1. Given that f(1)=2 and the slope at any point is dy/dx=5xyx2y25, we first need to determine the slope at x=1. However, there seems to be a typo in the expression for dy/dx. Assuming the slope should be dy/dx=5x2y25, at x=1, the slope dy/dx would be 5(1)2(2)25.

This suggests that the slope is positive at x=1, which usually indicates increasing function values and therefore suggests a relative minimum might occur there. However, without information on how the slope behaves for values of x other than 1, we cannot conclude definitively that x=1 is a relative minimum. Therefore, the correct answer is D. There is not enough information.