Find the equation of the line tangent to the graph of the given function at the point with the indicated x-coordinate.
f(x)=(4 sqrt(x)+7)/(sqrt(x)+2); text( ) x=4
y' = [(2/√x)(√x+2) - (4√x + 7)(1/(2√x))]/(√x+2)^2
y'(4) = (4 - 15/4)/16 = 1/64
y(1/64) = (4/8 + 7)/(1/8 + 2) = 60/17
Now you can use the point-slope form of the equation:
y - 60/17 = 1/64 (x - 4)