finding point where slope of line equals curve
1 Attachment(s)
1. The problem statement, all variables and given/known data
At what point on the curve y=2(xcosx) is the tangent parallel to the line 3xy=5. 3. The attempt at a solution 1. rewrite 3xy=5 as y3x5 2. equate 2(xcosx) = y3x5 3. differentiate: 2+2sinx = 3 4. solve for x: sin^1(,5) = 0.524 5. plug into y=2(xcosx) 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(xcosx) and y3x5 to see logically where the point of equal slope is ? Thanks for any help. 
Re: finding point where slope of line equals curve
Quote:
What you want is to find any point on the graph of y=2(xcosx) whose slope is 3, the slope ope of the line. Quote:
Quote:

Re: finding point where slope of line equals curve
You are right, there is an infinite number of solutions, solving for x gives you your answer or pi/6, and so the tangent of y=2(xcosx) is parallel to 3xy=5 whenever x=pi/6 +2pi*n where n is an integer. As said above, instead of considering the intersection of the two functions, you are looking for points where the tangent line (whose slope is the derivative of y=2(xcosx)) is parallel to 3xy=5.

Re: finding point where slope of line equals curve
thanks guys.
I understand what you are saying. So to clarify, when the question asks: at what point(s) on the curve is the tangent parallel to the line, then the answer would just be: "the tangent of y=2(xcosx) is parallel to 3xy=5 whenever x=pi/6 +2pi*n where n is an integer" ? i.e. I would not need to include y value reference in the answer ? 
Re: finding point where slope of line equals curve
To identify the points they're asking for, you need to supply a y value as well.

Re: finding point where slope of line equals curve
sorry to persist with this, but I just don't know how to express the recurring y values (due to the infinite amount of possible answers).
Can someone please show me to express the y values ? Perhaps I would just express the points as: x=pi/6 +2pi*n, y = f(pi/6 +2pi*n) x=3pi/6 +2pi*n, y = f(3pi/6 +2pi*n) 
Re: finding point where slope of line equals curve
Use the equation you're given: y = 2(x  cos(x))
If x = ##\pi/6## + 2n*##\pi## , then y = 2(##\pi/6## + 2n*##\pi## √3/2) 
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