Let $f(x, y) = ye^{x^2 - 6}$. Which of the following is the gradient of $f(x, y)$ at point $(4, 28)$?
a. $e<49, -8>$
b. $e<-49, 8>$
c. $e<49, -7>$
d. $e<-49, 7>$
Find parametric equations for the tangent line at the point $(3, 4, 5)$ to the curve which is the intersection of the surface
$x^2 + y^2 + z = 78$ and the plane $x = 3$.
a. $x = 3t, y = 1 - 4t, z = 32 + 5t$
b. $x = 3t, y = 1 + 4t, z = -32 + 5t$
c. $x = 3, y = 4 + t, z = 5 + 32t$
d. $x = 3, y = 4 + t, z = 5 - 48t$
Find a point on the surface $z = xy$ where the tangent plane is parallel to the plane $34x + 5y + z/2 = 10$.
a. $(68, 10, 680)$
b. $(-68, -10, 680)$
c. $(-10, -68, 680)$
d. $(10, 68, 680)$
