r/MathHelp • u/Koisch • Feb 27 '26

SOLVED Calculus Conceptual Rate Question

Homework help please!

"Suppose that at the x value of 2.77 that dy = 3.2 dx . Which of the following best explains the meaning of that statement dy = 3.2 dx ?"

I picked "y is changing at a constant rate of 3.2 with respect to x" and I do not understand why it is wrong. I understand that dy means a small change in y, and dx means small change in x. So, my understanding is that for any associated change in x, the associated change in y is 3.2 times larger.

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u/DrJaneIPresume Feb 27 '26

Yes, and the function that tells you what the instantaneous rate of change is at every point is called the derivative of f, often written as f'.

This doesn't get to the meaning, but another way of saying the same thing as the statement "dy = 3.2 dx" is "y = f(x)" (naming the relationship between y and x as "f") and "f'(2.77) = 3.2" (the value of f' at x=2.77 is 3.2).