In the Taylor series

find the number a in the next term by testing at x=0

OK, so, I take the 4th derivative of u(x): u''''(x)=24 and u''''(4)=24

Now I have as my next term, but how does that help me find the constant a? I'm confused.

Ah, wait a minute, I see it.

The term has a coefficient of 1. So and