Question

Please help! :)

For the function f(x) = 3/(x-4):

What is the equation of the tangent line to the curve f(x) at x = 1?

Answer 1

Is this a calculus question? If so, take the first derivative of f(x), which gives you the instantaneous slope as a function of x. Evaluate that at x=1 to find the slope, then use the formula \[y-y_0=m(x-x_0) \]to fit a line through the point of tangency. You'll have to evaluate \(y_0=f(x)\); you know \(x_0=1\).

Answer 2

That should be evaluate \(y_0=f(x_0)\) in case it isn't obvious...

Answer 3

\[\large f(x) = \large \frac{3}{x-4}\]\[\large f'(x) =\frac{d}{dx}[3(x-4)^{-1}] = 0-1(3)(x-4)^{-2} = -\frac{3}{(x-4)^2}\]\[\large f'(1)= -\frac{3}{(1-4)^2}=?\]