Question

If the graph of a differentiable function y = f (x) meets the lines y = – 1 and y = 1, then the graph ____________.

Options

• meets the line y = 0 at least twice

• meets the line y = 0 at least once

• meets the line y = 0 at least thrice

• does not meet the line y = 0

Answer 1

If the graph of a differentiable function y = f (x) meets the lines y = – 1 and y = 1, then the graph meets the line y = 0 at least once.

Explanation:

Because the graph cuts the lines y = -1 and y = 1, it must cut the line y = 0 at least once because the graph is in this case a continuous curve.