Question

First find the general derivative of f (x) = {√(x−1)} . Then find the
equation of the tangent line to the graph at x = 10.

Answer 1

df/dx = (1/2)(x-1)^-1/2
At x = 10, the slope is
df/dx = (1/2)/sqrt9 = 1/6

The value of f(x) at that point is
sqrt(9) = 3

You want a line that passes through (10,3) with slope = 1/6. Its equation can be written

y - 3 = (x - 10)*(1/6)

Rewrite that in standard form, if necessary.