Haru S.

asked • 01/09/23

Calculus: Rate of Change

(Referencing Review Set 19A, Q9)

I am struggling with part b

Question: An equilateral triangle has side length x cm and area A cm2. Th side length of the triangle is increasing at 3 cm per minute.

a) State the relationship between A and x.

b) At what rate is the area increasing when the side length is 15cm?


Answer:

a) A=x2root3/4 <-- I was able to get this answer.

b) 45 root3/2 cm2 per minute.

1 Expert Answer

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Chikae Y. answered • 01/09/23

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Haru S.

Thank you for the video! I have one question. For the equation, "dA/dt=xroot3/2 x dx/dt", why is dx/dt multiplied? I thought dA/dt was directly equal to xroot2/3.
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01/09/23

Chikae Y.

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Hi Haru - because we're taking the derivative of the expression implicitly *with respect to time (t)*, when we do the chain rule, you have to also take the derivative of "x" with respect to t (which is dx/dt) If you think about the types of differentiation problems you probably started with, you probably solved everything as dy/dx, right? So that means that you were taking the derivative of everything with respect to x. So technically speaking, there was a "dx/dx" at the end of each of those problems too... but that equals 1, so we never write it.
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01/09/23

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