Find an equation of the tangent line to the curve at the given point. y = 4x/(x + 2) , at point (2, 2)

Answer 1

Finding a tangent line at the point (2,2) for the given curve can be solved via the following concepts:

1.) Take the derivative of the curve and find the slope at (2,2)

2.) Find the y-int for the tangent line using the point (2,2)

Part (1.) is done by remembering the derivative steps one takes for a given fraction:

y = (4x)/(x+2) -> y' = ((x+2)*(4)-(4x)*(1))/(x+2)^2

Thus y' = 8/(x+2)^2 -> The slope being y' = 8/(4)^2 = 0.5

The slope for the equation y= mx+b gets m = 0.5

For the 'b' value, use the (2,2) point as follows: 2 = 1/2*2 + b, where b = 1

Thus your tangent line equation results as: y = 0.5(x) + 1