Question
The slope of a function f (x) at any point (x, y) is \(\frac{x-3}{x^{2}-3x-4}\) The point \(\left ( 5,\frac{4}{5}\ln 6 \right )\) is on the graph of f (x).
(A) Write an equation of the tangent line to the graph of f (x) at x = 5.
(B) Use the tangent line in part (a) to approximate f (4.5) to the nearest thousandth.
(C) Find the antiderivative of \(\frac{\mathrm{d} f}{\mathrm{d} x}=\frac{x-3}{x^{2}-3x-4}\) with the condition \(f(5)=\frac{4}{5}\ln 6\).
(D) Use the result of part (c) to find f (4.5) to the nearest thousandth.
Answer/Explanation
