posted this in a question and answers forum , and someone proved that g(0)=0 does not always hold?here's the link http://math.stackexchange.com/questions/463839/prove-that-g0-0
this is fishy , spivak didn't even include the solutions of this question after i cehcked the solutions book
Homework Statement
Hello,
Suppose that f and g are differentiable functions satisfying
##\displaystyle \int_{0}^{f(x)} (fg)(t) \, \mathrm{d}t=g(f(x))##
Prove that g(0)=0
now if f(x)=0 in some point then it's straigh forward that g(f(x))=g(0)=0 anyways:
differentiating the first formula we get...