Find the point on the curve y=cosx closest to the point (0,0)?
1 Answer
May 13, 2018
The point is
Explanation:
By the distance formula, the distance between
d= sqrt((x -0)^2 + (cosx - 0)^2)
d = sqrt(x^2 + cos^2x)
To find the minimum distance, we need to differentiate.
d' = (2x - 2cosxsinx)/(2sqrt(x^2 + cos^2x))
d' = (x - cosxsinx)/sqrt(x^2 + cos^2x)
We wish for this to be the smallest possible, thus we need
0 = (x - cosxsinx)/sqrt(x^2 + cos^2x)
0 = x - cosxsinx
Use a graphing application to solve and find that
There derivative is negative when
Hopefully this helps!