Let ( W= left {p(x) in P_{n} mid p(x) right. ) has a horizontal tangent at ( left.x=0 right } ). (a). Show ( W ) is a subspace of ( P_{n} ). (14 points) (b). Find a basis for this subspace. (10 points)

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Let  ( W= left {p(x)  in P_{n}  mid p(x) right.  ) has a horizontal tangent at  (  left.x=0 right }  ). (a). Show  ( W  ) is a subspace of  ( P_{n}  ). (14 points) (b). Find a basis for this subspace. (10 points)

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(Solved): Let \( W=\left\{p(x) \in P_{n} \mid p(x)\right. \) has a horizontal tangent at \( \left.x=0\right\ ...

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