The function g is defined for x>0 with g(1)=2, g'(x)=sin(x+1/x), and g"(x)=(1-1/x^2)cos(x+1/x).

A. Find all values of x in the interval 0.12<=x<=1 at which the graph of g has a horizontal tangent line.

B. On what subintervals of (0.12,1), if any, is the graph of g concave down? Justify you answer.

C. Write an equation for the line tangent to the graph of g at x=0.3.

D. Does the line tangent to the graph of g at x=0.3 lie above or below the graph of g for 0.3<x<1? Why?

I have no clue how to solve this. Can you please help me step by step. Thanks

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