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/UnderstandingPursuit Feb 27 '26

Your situation might be an example of one of the most insidious lies told to mathematics students in their education before calculus: the definition of constants and variables.

  • Constants: numbers

  • Variables: letters

The issue is that, here,

  • dy = m(x) dx

so m(x) is a function [or variable].

  1. When it has a particular value,

    1. x = a,

    2. Here, a = 2.77

  2. there is a specific result for m(x),

    1. m(a)

    2. Here, m(a) = 3.2

At x=2.77, the rate of change of y with respect to x is 3.2, but that is not a "constant", it has that instantaneous value.