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The question that I am stuck at goes like this:

On the curve $y^3=27x$, the absolute value of rate of change of ordinate is greater than the absolute value of rate of change of abscissa in the interval:

  1. $(-\infty, -3)$
  2. $(-3,3)$
  3. $\phi$
  4. $(3,\infty)$

The answer is given as option (2). The detailed solution is given as:

enter image description here

Now what I don't understand is:

I tried plotting this problem in GeoGebra. (the function input is same as the original function in the question)

Problem

From the question I inferred that they asked in which interval $\frac{dy}{dx}>1$. Fine!

From the graph, it looks like (-1,1) should be the interval, which does not coincide with the answer given.

Did I miss out on anything?

Please let me know if I have erred in my way of asking this question so that I can improve. Also please forgive any blunders in my way of asking questions. Your feedback is crucial.

You may refer my profile for my level.

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Be careful. It's true that we're looking for points on the graph of $y^3 = 27x$ where $\frac{\mathrm{d}y}{\mathrm{d}x} > 1$, and indeed those are the points where $x \in (-1, 1)$.

But the answer is looking at the ordinates, i.e. $y \in (-3, 3)$.

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  • $\begingroup$ Oh, thanks! I did not get it then, but now I got your point. $\endgroup$
    – Harikrishnan M
    Commented Dec 30, 2023 at 7:31

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