I just wanted to check my answer and to see if I'm doing this right as well as get help on the b.

Let f be the function with f(1) = 4 such that for all points (x,y) on the graph of f the slope is [3x^2 + 1]/2y

A) Write an EQ for line tangent to graph @ x=1 and use it to approximate f(1.2)

B) f(1.4) may also be approximated using the line you computed in A, which is a better approximation f(1.2) or f(1.4) ?
A) y - 4 = ((3(1)+1)/2(4))(x-1)
y - 4 = 1/2 (x-1)
2y - 8 = x - 1
2y - x = 7

Substituing 1.2 for x, 2y - 1.2 = 7 so then f(1.2) = 4.1

B) I think f(1.2) would be a better approximation since it's closer to the inital x, 1