Explain why or why not Determine whether the following statementsare true and give an explanation or counterexample.a. For a function ƒ of a single variable, if ƒ'(x) = 0 for all x in the domain, then ƒ is a constant function. If ∇ ⋅ F = 0 for all points in the domain, then F is constant.b. If ∇ x F = 0, then F is constant.c. A vector field consisting of parallel vectors has zero curl.d. A vector field consisting of parallel vectors has zero divergence.e. curl F is orthogonal to F.

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