Max heap and array relation This question is about max heap and array


  Suppose there is max heap $h$, with $n$ data items already stored in $h$. An array that is formed by inserting a value larger than all the values in $h$ at the beginning/head of the heap $h$ is assumed to be new array $C$. 
  The array $C$ is a heap  (or)  not?


My answer: is heap because it's bigger than any other element in array


  With $n$ data items already stored in heap $h$, a new array $D$ is created by adding a value $u$ to the heap $h$ that is smaller than any of the $n$ items already stored in heap. If $u$ is added to last element in heap $h$, is array $D$ heap or not?


My answer: it is heap because the smallest one has to be in the leaf

But what is the relation with array? Is there rule to insert node in heap? 
I know that to insert node to array in heap we insert data as last element of heap and then put it in the root and heapify it.
Suppose an array $A$ is a maxheap.  Inserting a large element in the first position of $A$ does not necessarily preserve the maxheap property.  The maxheap property requires a node's value to be larger than both its children's values, for each node in the tree.  If the value inserted in the first position is larger than all values in the array, then the maxheap property is preserved at the root node, but might not be preserved at some of the other (lower level) nodes. 

We can construct an initial array $A$ such that the nodes in the subtree rooted at the right child of the root have much larger values than the nodes in the subtree rooted at the left child of the root. When a new value is inserted in the first position of the array, the tree changes so that the smaller values in the left subtree become parents of the larger values in the right subtree, causing the maxheap property to be violated. For example, take $A=[6,3,5,2,1,4]$, which is a maxheap.  Inserting a $7$ in the beginning modifies $A$ to $A=[7,6,3,5,2,1,4]$, which is not a maxheap because the node with value $3$ is a parent of the node with value $4$.