Another form of Rolle’s theorem for the continuous condition is

The correct option is f is continuous on [a,a+h].

Step-by-step Explanation:

Rolle's Theorem is traditionally stated for a function defined on a closed interval. The standard continuity condition requires the function to be continuous on the closed interval:

$[a,b]$

We can rewrite the upper limit of the interval by introducing a step size or increment represented by:

$h$

If we define the relation between the endpoints as:

$b=a+h$

Then, substituting this expression for the upper bound into the interval gives:

$[a,a+h]$

Consequently, the corresponding condition for this form of the theorem is that the function must be continuous on the closed interval:

$[a,a+h]$