Asked by x
Find the parabola of the form y=ax^2 +bx that shares a tangent line with the function y= (2x)/(x^2 +1) when x=1. Solve and show all steps.
Answers
Answered by
oobleck
First, the tangent line.
y = (2x)/(x^2+1)
y' = -2(x^2-1)/(x^2+1)^2
At x=1, y=1 and y'=0
So, the tangent line at x=1 is the line y=1
Now, surely you can come up with a parabola which has its vertex at (1,1) and goes through the origin.
y = (2x)/(x^2+1)
y' = -2(x^2-1)/(x^2+1)^2
At x=1, y=1 and y'=0
So, the tangent line at x=1 is the line y=1
Now, surely you can come up with a parabola which has its vertex at (1,1) and goes through the origin.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.