If

represent a family of surfaces for different values of the constant

. The gradient of the function

defined as

is a vector normal to the surface

.
Given <span>the paraboloid

.
We can rewrite it as a scalar value function f as follows:

The normal to the </span><span>paraboloid at any point is given by:

Also, the normal to the given plane

is given by:

Equating the two normal vectors, we have:
</span>

Since, -1 = 2 is not possible, therefore
there exist no such point <span>
on the paraboloid
such that the tangent plane is parallel to the plane 3x + 2y + 7z = 2</span>
.
The answer to the problem is A
Answer:
Rational and integer i.e option A and C
Propane costs $3.50 per hundred pounds,
and there is a $6 monthly delivery fee.
A family has budgeted $85 for their propane this month.
Let 'x' hundreds of pounds can the family use without going over budget
Here family has budgeted $85 for their propane.
So the cost for Propane = $ 3.5x
One month delivery fee $6
Therefore cost + delivery charge not exceed $85
So 3.5x + 6 ≤ 85
3.5x=85-6 =79
x = 22.57
Therefore 22 hundreds of pounds can the family use without going over budget