Answer to Question #54820 in Real Analysis for Thekra

Question

Q1:
f is differentiable at c, prove that:
1) f′(c)=limh→0((f(c+h)−f(c)0\h)
2)f′(c)=limh→0(9f(c+h)−f(c−h))\2h)


Q2:
Let f:R→R .The function f is even if f(−x)=f(x) for all x∈R, and odd if f(−x)=−f(x) for all x∈R. if f is differentiable, prove that f′ is odd when f is even, and when f is odd.