A curve is such that dy/dx= 6/x^2 and (2,9) is a point on the curve. Find the equation of the curve.

Question

The slope of the curve has to be found by the dy/dx= 6/x^2. It will most likely end up as a y-y1=m(x-x1) formula at the end. 

Answer 1

dy/dx = 6/x²

 

To find y, take the indefinite integral of dy/dx

 

y = 6∫dx/x² = (-6/x) + C where C is a constant.

 

To find C, plug in the known point (2,9):

 

9 = (-6/2) + C

 

9 = -3 + C

 

12 = c

 

So:

 

y = (-6/x) + 12