If f(1) > 0 and f(3) < 0, then there exists a number c between 1 and 3 such that f(c) = 0. Is this true or false?

Question

Please and thank you

Answer 1

Absolutely true, uuuuhhh, if f(x) is continuous.

Answer 2

Can you please explain why it is true

Please and Thank you

Answer 3

If the curve is continuous, and at x=1 f(x) is positive, and at x=3, f(x) is negative, somewhere it crossed the axis.