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.
equation of the tangent line to the graph at x = 10.
Answers
drwls
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.
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.