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.
Okay, y= x^1/4)
Oh dear, no! If y= x^(1/4) then y' is NOT the same thing!y' = x ^ 1/4
I know that's not what you meant to say, but is is what you actually said. Be careful what you write. Mathematics is very precise.
What you meant to say was
No, the slope or derivative at x= 1 is (1/4)1^(-3/4)= 1/4. It is a constant, not a function of x.y'= 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)= (1/4)- 1/4. Adding 1 to both sides, y= (1/4)x+ 1- 1/4= (1/4)x+ 3/4.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.