Answer is D. Draw a line y=x. Now, the function can never touch the line as f'(x) is not equal to one. If you try to draw some random graph of function, while keeping in mind that its derivative is never unity, then there comes only one possibility where f(x) crosses the y=x line.
Take different f(a) and f(b) values, then you will notice if f(x) is only to one side of y=x line(make a rectangle of sides a and b), then it will necessary have a unit slope at some point. So, it will have to cut the line but only once.