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

4: Suppose \(b \in R\). Show that the set of continuous real-valued functions \(f\) on the interval \([0,1]\) such that \(\int_{0}^{1}f=b\) is a subspace of \(\mathbb{R}^{[0,1]}\) IFF \(b=0\)

Additive Identity:

assume \(\int_{0}^{1}f=b\) is a subspace