Explanation:
Continuous functions are those functions which do not have any abrupt breaks or jumps in their graph and the graph can be drawn without lifting the pen. For example, the function f(x) = x^2 is a continuous function as its graph is a smooth curve without any breaks or jumps.

Option A: Every continuous function is increasing
This statement is false. A continuous function can be increasing, decreasing, or neither. For example, the function f(x) = -x^2 is a continuous function but it is decreasing.

Option B: Every continuous function is decreasing
This statement is also false. A continuous function can be increasing, decreasing, or neither. For example, the function f(x) = x^3 is a continuous function but it is increasing.

Option C: Every continuous function is not differentiable always
This statement is true. There are many continuous functions that are not differentiable. For example, the function f(x) = |x| is a continuous function but it is not differentiable at x = 0. Another example is the function f(x) = √x, which is continuous but not differentiable at x = 0.

The reason for this is that the derivative of a function at a point is defined as the slope of the tangent to the graph of the function at that point. If the function has a sharp corner or cusp at that point, then the tangent does not exist and therefore the derivative does not exist.

Option D: Every continuous function is differentiable
This statement is false. As we have seen above, there are many continuous functions that are not differentiable.

Conclusion:
The correct option is C, as every continuous function is not differentiable always.