p p
1. For 1≦p＜∞ , show that the L norm arises from a scalar product of L (R)
if and only if p=2.
2 3 4
2. Let p(x)=a0+ a1x + a2 x +a3 x + a4 x be a polynomail with real
coefficients such that p'(x)>0 p"(x)>0 , p'''(x)>0 on [0,1].
3
If t=(t1,t2,t3) in R , t1+t2+t3=1 0≦ti≦1
Minimize g(t):= p(t1)+p(t2)+p(t3).
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