Identifying first negative number in array of doubles
I believe the parameter names val and array are switched around.  An array shouldn't be a single variable, and a value shouldn't be an array.  Otherwise, the names themselves are okay.
It's preferred to index through a C-style array with an std::size_t, especially if the array size is larger than an int.  This could be helpful if you'll be working with very large numbers, although the recursion aspect here may render that unlikely.  Even if you're not, it's best to develop that habit.
This looks a bit misleading:

if(val[instance] &lt; 0) return instance;
instance++;


At first, I thought the instance++ was missing indentation and belonged to the if statement.  To make this clearer, you could separate the two lines or, even better, have curly braces for the if statement.  The latter also helps with better maintainability.

if (val[instance] &lt; 0)
{
    return instance;
}

instance++;

Again, some of the naming is misleading:

if(array &lt; 1) return 0;


From a glance, that just looks incorrect as you cannot check an array like that.  Proper naming is very important, even for a small program like this.