Arc Length of y = f(x) on [a, b] is at least b - a

[PaulErly]

I just need help on this "Just for Fun" question my math teacher gave me. If someone could solve it so I could just see how it works, that would be great.

I think I'm just making it harder on myself than it actually is;

Show that the arc length of y = f(x) on [a, b] is at least b - a, where f' is continuous on [a, b]

Thanks!

 

[pka]

The arc length is \(\displaystyle s = \int\limits_a^b {\sqrt {1 + \left[ {f'(x)} \right]^2 } dx}.\)

Here is a big hint: \(\displaystyle \sqrt {1 + \left[ {f'(x)} \right]^2 } \ge 1.\)


P.S.
\(\displaystyle \L \left[ {\forall x \in [a,b]} \right]\left( {g(x) \le f(x) \Rightarrow \int\limits_a^b g \le \int\limits_a^b f } \right)\)