Mth301 Quiz 2 Fall 2024

1. Question: If the partial derivative (w.r.t ‘x’ or ‘y’) at any point on the surface: “z = f(x, y)” is zero, then the tangent plane at that point will be __________ to the XY-plane.

   • Answer: parallel

2. Question: The surface $z=f(x,y)$ falls (decreases) most rapidly at any point in the __________ of Gradient(z).

   • Answer: Opposite to the direction

3. Question: The surface $z=f(x,y)$ neither falls nor rises (decreases or increases) at any point in the __________ of Gradient(z).

   • Answer: Direction perpendicular to

4. Question: The equation of the line that passes through the point (0, 1) and has a slope of 2 is:

   • Answer: 2x + y - 1 = 0

5. Question: Let $m$ be the slope and $c$ be the y-intercept, then the slope-intercept form of the equation of a line is __________.

   • Answer: y = mx + c