Find the slope of the tangent line to the curve that is the intersection of the surface z = x² - y² with the plane x = 2 at the point (2, 1, 3). A) -2 B) 2 C) 0 D) -4 E) 4

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Quizplus · Accepted Answer

The given surface is $z = x^{2} - y^{2}$. To find the slope of the tangent line to the curve of intersection with the plane $x = 2$, we substitute $x = 2$ into the equation of the surface, getting $z = 2^{2} - y^{2} = 4 - y^{2}$. The derivative of $z$ with respect to $y$ gives the slope of the tangent line at any point $y$, which is $\frac{dz}{dy} = -2y$. At the point (2, 1, 3), $y = 1$, so the slope is $-2(1) = -2$.

Find the Slope of the Tangent Line to the Curve