Originally Posted by

**MrJank** (3) For each of the mysterious functions below, use the given properties to find a,b,c.

(a) f(x) = ax^2+bx=c, where f(1)=3 f`(0) = -1 f`(1) = 2.

Now, I think I'm comfortable doing this with 3 points of f(x), but I'm confused as to how to do this with 1 or more points of f`(x).

Normally, I would create an augmented matrix and plug the points in, but again I don't know what to do with the f`(x) points.

(b) g(x) = asin(x) + bcos(x) +c where, g(0) = 2 g(pi)=1 g`(0)=-2

(c) h(x) a +b(e^x) + c(e^-x) where, h(1)=e^2+1 , h`(1) = e^2 - 1 integral of h(x)dx = e^2 from 0 to 1