APFIVE Tangent Line Approximation
Let $$y = f(x)$$ be a differentiable function such that $$\displaystyle\frac{dy}{dx} = \frac{2x+1}{y}$$ and $$f(1) = 3$$. What is the approximation for $$f(0.9)$$ found by using the tangent line to the graph of $$f$$ at $$x=1$$?
A
$$3.3$$
B
$$3.1$$
C
$$2.9$$
D
$$2.7$$
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