9514 1404 393
Answer:
10x +9y = 60
Step-by-step explanation:
The equation for the tangent line at a point is ...
y -f(a) = f'(a)(x -a)
For the given function,
f(x) = 10/x
The derivative is ...
f'(x) = -10/x^2
Then the equation of the tangent line is ...
y -10/3 = -10/9(x -3) . . . . equation of the tangent line (point-slope form)
Clearing fractions, we have ...
9y -30 = -10(x -3) = -10x +30
10x +9y = 60 . . . . . equation in standard form
