Question

Let $f(x, y) = 16 - 2x^2 - y^2$ A) $f_x(x, y) = -4x$ B) $f_y(x, y) = -2y$ C) Find the direction vector for the line tangent to the trace $f(x, -1)$ at $x = 1$ $\<1, 0, -4>$ D) Find the direction vector for the line tangent to the trace $f(1, y)$ at $y = -1$ $\<0, 1, 2>$ E)Find parametric equation in $R^3$ for the tangent line to the trace $f(x, -1)$ at $x = 1$. $r(t) = (1, -1, 13) + <1, 0, -4>t$ F)Find parametric equation in $R^3$ for the tangent line to the trace $f(1, y)$ at $y = -1$. $r(t) = (-1, 1, 0) + <0, 1, 2>t$ G) Find the equation of the plane that passes through the point $(1, -1, f(1, -1))$ and whose normal vector is orthogonal to the direction vectors found in (C) and (D) z =

          Let $f(x, y) = 16 - 2x^2 - y^2$
A) $f_x(x, y) = -4x$
B) $f_y(x, y) = -2y$
C) Find the direction vector for the line tangent to the trace $f(x, -1)$ at $x = 1$
$\<1, 0, -4>$
D) Find the direction vector for the line tangent to the trace $f(1, y)$ at $y = -1$
$\<0, 1, 2>$
E)Find parametric equation in $R^3$ for the tangent line to the trace $f(x, -1)$ at $x = 1$.
$r(t) = (1, -1, 13) + <1, 0, -4>t$
F)Find parametric equation in $R^3$ for the tangent line to the trace $f(1, y)$ at $y = -1$.
$r(t) = (-1, 1, 0) + <0, 1, 2>t$
G) Find the equation of the plane that passes through the point $(1, -1, f(1, -1))$ and whose normal vector is orthogonal to the direction vectors found in (C) and (D)
z =

Let f(x, y) = 16 - 2x^2 - y^2
A) fx(x, y) = -4x
B) fy(x, y) = -2y
C) Find the direction vector for the line tangent to the trace f(x, -1) at x = 1
1, 0, -4>
D) Find the direction vector for the line tangent to the trace f(1, y) at y = -1
0, 1, 2>
E)Find parametric equation in R^3 for the tangent line to the trace f(x, -1) at x = 1.
r(t) = (1, -1, 13) + <1, 0, -4>t
F)Find parametric equation in R^3 for the tangent line to the trace f(1, y) at y = -1.
r(t) = (-1, 1, 0) + <0, 1, 2>t
G) Find the equation of the plane that passes through the point (1, -1, f(1, -1)) and whose normal vector is orthogonal to the direction vectors found in (C) and (D)
z =

Added by James O.

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