So, I have been working problems finding the derivative of polynomial equations. I am having some problems, however. The problem is as follows:
Find the line tangent to the curve of Y = 4th root of X, on the point (1, 1).
This is my working of the problem...
y= 4th root of x
y' = x ^ 1/4 = 1/4 x ^ -3/4 = m
therefore, the line tangent to this should be Y - Y1 = m(x - x1) so:
y - 1 = 1/4 x ^ -3/4(x - 1)
y - 1 = 1/4 x ^ 1/4 - 1/4x ^ -3/4
y = 1/4 x ^ 1/4 - 1/4x ^ -3/4 + 1
y = 1/4x + 1 <<<<<<
So by my calculations the line equation should be y = 1/4x + 1. However the book has the answer as y = 1/4x + 3/4. Where have I gone wrong? I don't see it.