(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

At what point on the curve y=2(x-cosx) is the tangent parallel to the line 3x-y=5.

3. The attempt at a solution

1. rewrite 3x-y=5 as y-3x-5

2. equate 2(x-cosx) = y-3x-5

3. differentiate: 2+2sinx = 3

4. solve for x: sin^-1(,5) = 0.524

5. plug into y=2(x-cosx) to get y value: y = -0.684

I am not sure I have this correct though. At stage 4 above, I have a trig equation. So doesn't that give me an infinite number of solutions. (I was not given a range in this question). Or do I just look at the graph of 2(x-cosx) and y-3x-5 to see logically where the point of equal slope is ?

Thanks for any help.

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# Finding point where slope of line equals curve

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