Quod Erat Demonstrandum


What’s wrong?

Filed under: Additional / Applied Mathematics,NSS — johnmayhk @ 7:05 下午
Tags: ,

Here is a basic level M2 question:

Given that \sqrt{xy}=7+2y, find \frac{dy}{dx} at (-\frac{1}{3},-3).

Student 1 gave




Thus, at (-\frac{1}{3},-3),


Student 2 gave

\sqrt{x}\cdot \frac{1}{2\sqrt{y}}\cdot \frac{dy}{dx}+\sqrt{y}\cdot \frac{1}{2\sqrt{x}}=2\frac{dy}{dx}


Thus, at (-\frac{1}{3},-3),



The answer obtained above is wrong.

By using Desmos, the shape of the equation \sqrt{xy}=7+2y can be easily seen below,

thus \frac{dy}{dx} at (-\frac{1}{3},-3) should be negative, in fact, the correct answer is -\frac{9}{13}.

Students, what’s wrong there?

Think about that:

1. Is it always true that \frac{x}{\sqrt{xy}}=\sqrt{\frac{x}{y}} ?

2. Is it always true that \sqrt{xy}=\sqrt{x}\sqrt{y} ?

Also read

1 則迴響 »

  1. Good example. Note that there is a typo in the first line of Student 1’s answer, a factor 1/2 is missing.

    迴響 由 Wilson Cheung Wai-Shun — 2019/05/05 @ 9:55 下午 | 回應

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