(Solved): 2) The graph of the curve x2+2xyy2+x=2 and its tangent line at (1,0) are shown below. The curve ...

2) The graph of the curve $x^2+2xy-y^2+x=2$ and its tangent line at $(1,0)$ are shown below. The curve is red and the tangent line is blue: a) The slope of a curve at a point is the slope of the line tangent to the curve at that point. Use the graph of the tangent line to determine the slope of $f(x)$ at the point where $(1,0)$. Use the slope formula or a rise/run calculation. b) Use implicit differentiation to find $\frac{dy}{dx}$. c) Use $\frac{dy}{dx}$ to find the slope of the curve at $(1,0)$. d) Find the equation of the line tangent to the curve at $(1,0)$.