Find an equation of the tangent line to the graph of f(x)=x+3/x^2+2

Question

at x=1
A.5x+9y=17
B.5x+3y=9
C.9y-5x=7
D.5x+9y=7

Answer 1

I will assume you meant:
f(x)= (x+3)/(x^2+2)

then f(1) = 4/3, so the point you want is (1, 4/3)

f'(x) = ( (x^2 + 2)(1) - (x+3)(2x) )/(x^2 + 2)^2
f'(1) = (3 - 8)/9 = - 5/9

tangent: y - 4/3 = (-5/9)(x - 1)

simplify to see which of the choices matches

Answer 2

Find an equation of the line tangent to the graph of x^2+(y-x)^3=9 at x=1