Let V be the vector space of differentiable functions on 0, 1| with continuous derivative. Which properties of a norm are satisfied for the function || f(x)|| = max f(x)+max f' (x)| on V? (0,1) [0,1] O || F|| = 0 if ƒ = 0 and || f|| > 0 if f + 0. O ||af|| = |a| · || f|| for all real a. O || f + g|| < || ||+ |||

Elementary Linear Algebra (MindTap Course List)
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Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
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Let V be the vector space of differentiable functions on 0, 1 with
continuous derivative. Which properties of a norm are satisfied for the
function || f(x)|| = max |f(x)|+ max |f' (x)| on V?
([0,1]
[0,1]
O ||f|| = 0 if ƒ = 0 and || f|| > 0 if f + 0.
O ||af|| = |a| · || f|| for all real a.
O || f + g|| < || ||+ |||
Transcribed Image Text:Let V be the vector space of differentiable functions on 0, 1 with continuous derivative. Which properties of a norm are satisfied for the function || f(x)|| = max |f(x)|+ max |f' (x)| on V? ([0,1] [0,1] O ||f|| = 0 if ƒ = 0 and || f|| > 0 if f + 0. O ||af|| = |a| · || f|| for all real a. O || f + g|| < || ||+ |||
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