APFIVE Tangent Line for an Integral Function
Let $$f$$ be the function defined by
$$f(x)=\int_{\pi/6}^{x}\tan t\, dt.$$
Which of the following is an equation for the line tangent to the graph of $$f$$ at the point where $$x=\frac{\pi}{6}$$?
A
$$y=\frac{1}{2}\left(x-\frac{\pi}{6}\right)$$
B
$$y=0$$
C
$$y=\frac{\sqrt{3}}{3}\left(x-\frac{\pi}{6}\right)$$
D
$$y=x-\frac{\pi}{6}$$
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