what are the points of tangency to the curve y= ln (x-1 / x+1), where the slope of the tangent is 0.25?

Question

what are the steps?

Answer 1

Hello, thank you for taking the time to post your question!

The starting point on a question like this would be finding the derivative of the function then setting it equal to the indicated slope value.

So the derivative of the function here would be dy/dx = 2 / (x^2 – 1)

Setting that equal to 0.25 and then solving I get

2 / (x^2 – 1) = 0.25

2 = 0.25x^2 – 0.25

2.25 = 0.25x^2

9 = x^2

x = -3 and x = +3

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)