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## Summary:

- Show that the set of differentiable real-valued functions ##f## on the interval ##(-4,4)## such that ##f'(-1) = 3f(2)## is a subspace of ##\mathbb{R}^{(-4,4)}##

Problem:

This is my first bouts with rigorous mathematics and my brain is not at all wired for attacking problems like this (yet). I know that a subspace ##U## of vector space ##V## must satisfy the conditions that ##0 \in U##, and for ##u, w \in U \Rightarrow u + w \in U## and lastly ##a \in \mathbb{R}## and ##u \in U \rightarrow au \in U## (additive identity, closed under addition, closued under scalar multiplication respectively).

How do I attack this intelligently? What question do I need to ask myself?

**Show that the set of differentiable real-valued functions ##f## on the interval ##(-4,4)## such that ##f'(-1) = 3f(2)## is a subspace of ##\mathbb{R}^{(-4,4)}##**This is my first bouts with rigorous mathematics and my brain is not at all wired for attacking problems like this (yet). I know that a subspace ##U## of vector space ##V## must satisfy the conditions that ##0 \in U##, and for ##u, w \in U \Rightarrow u + w \in U## and lastly ##a \in \mathbb{R}## and ##u \in U \rightarrow au \in U## (additive identity, closed under addition, closued under scalar multiplication respectively).

How do I attack this intelligently? What question do I need to ask myself?

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