Checkpoint 2

In Figure C1 we show the graph of the equation ${\displaystyle y^2-x^2=1}$.

Figure C1   Graph of ${\displaystyle y^2-x^2=1}$

1. Use the method of implicit differentiation to find the slope of the tangent line to the curve at ${\displaystyle x=1}$ and ${\displaystyle y=\sqrt{2}.}$

2. Use the explicit method of Checkpoint 1 to find the slope of the tangent line to the curve ${\displaystyle (1,\sqrt{2}).}$