CBSE Class 12-science Answered

Slope" in one dimension can be represented by one number, namely how
fast the curve is going up as you move to the right. In two dimensions
(3-D plot), you need 2 numbers to determine the slope. One indicates
how quickly the surface rises as you increase x, and the other, how
quickly the surface rises as you increase y. For "nice" functions,
these two numbers are enough to determine the rate of rise moving in
any direction in the x-y plane.

Mathematicians usually don't think of a two-numbered slope, though. 
It's best to re-think what slope means in one dimension as the line
that just touches the curve at the point in question. The slope of
this line is the slope of the curve. In 2-D, instead of a line tangent
to a curve, think of a plane tangent to the surface. That tangent
plane is what's usually worked with.

In higher-dimensional geometry, one can define the tangent plane for a surface in an analogous way to the tangent line for a curve. In general, one can have an (n − 1)-dimensional tangent hyperplane to an n-dimensional manifold.