Chapter 4.3, Problem 64E

The sine integral function

$\text{Si}\left(x\right)={\displaystyle {\int }_0^x\frac{\sin t}{t}}dt$

is important in electrical engineering. [The integrand f(t) = (sin t)/t is not defined when t = 0, but we know that its limit is 1 when t  → 0, So we define f(0) = 1 and this makes f a continuous function everywhere.]

1. (a) Draw the graph of Si.
2. (b) At what values of x does this function have local maximum values?
3. (c) Find the coordinates of the first inflection point to the right of the origin.