a. For the following function, find f (a).

Question

b. Determine an equation of the line tangent to the graph of f at (a,f(a)) for the given value of a.
f(x)= 9/(x+4) ,a=2

Answer 1

f'(x) = -9/(x+4)^2
at x=2, f'(2) = -1/4
f(2) = 3/2
so now you have a point (2,3/2) and a slope (-1/4) so the point-slope equation for the tangent line is
y - 3/2 = -1/4 (x-2)