Question

When gradient of a function is zero, the function lies parallel to which axis?"?

Answer 1

Gradient of a any function is a Slope...If gradient of a function is zero...it means Slope of that function is zero...

if slope is zero then a line must be parallel to x- axis...

This can be explained as follow..

Suppose we have a function f(x) = 2 ( we can take any constant or consider a constant function)

Now f(x) = 2 also can be written as y = 2 which is nothing just a line parallel to X-Axis...If we differentiate the function f(x) with reapect to x we get
d ( f ( x ) ) / dx = 0

Here d ( f ( x ) ) / dx is nothing just a gradient or slope of a function f (x)...

gradient = slope = d ( f ( x ) ) / dx = 0
=> line is parallel to x-axis...

hope this help......