For each statement below, either give a proof that the statement is true or give a counter- example to show that the statment is false (a) The curl of the gradient of a C2 function equals the zero...

Please solve part (c) of the problem.

Extracted text: For each statement below, either give a proof that the statement is true or give a counter- example to show that the statment is false (a) The curl of the gradient of a C2 function equals the zero vector (b) The divergence of the curl of a C2 vector field equals 0. (c) The divergence of the gradient of a C2 function equals 0