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## Homework Statement

Find a formula for one function that satisfies these given conditions:

1.)

*f*is continuous on [0,1].

2.) f(0) = f(1) = 0 (exactly).

3.) f(x) is greater than or equal to 0 for [0,1]

4.) The area under the graph of

*f*from 0 to 1 is equal to 1 (exactly).

Calculate the arc length.

Try to find the smallest possible arc length.

## Homework Equations

Arc Length formula

## The Attempt at a Solution

I don't know! I'm completely lost. So far I found the function f(x) = -6x^2+6x gives me an arc length of ~3.249 and satisfies all four conditions. But I'm pretty sure there must be a smaller arc length. Please help me find the smallest possible arc length. Thank you!