Define the following norm for f∈C1([0,1])f∈C1([0,1]), the vector space of continuously differentiable functions f:[0,1]→Rf:[0,1]→R,
∥f∥∗=|f(0)|+∥f′∥∞.(∗)(∗)‖f‖∗=|f(0)|+‖f′‖∞.
(a) Verify that if f∈C1([0,1])f∈C1([0,1]) with ∥f∥∗=0‖f‖∗=0, then f(x)=0f(x)=0 ∀x∀x. Justify all steps.