It is interesting that "sin(3x)" does something meaningful in Mma's other input methods.

In so-called free-form input, sin(3x) is recognized and converted into the syntactically correct form (i.e. Sin[3x]). Use "plot sin(3x)", which Mma would not understand at all, emits the correct syntax (i.e. Plot[Sin[4x], {x, -2,2}] as well a nice plot and some other good info.

In "Wolfram | Alpha query" mode, the same syntax is recognized and it emits several nice plots, although it does not supply the Mma syntax (that makes the plots).

Of course, submitting the minimize command above does not get anything meaningful except the various forms the Minimize[] function takes.

BTW, the free-form input can be reached by starting with a single equal-sign. And W|a query mode can be reached by starting with 2 equal-signs.

Regards..

Congruent Light
http://congruentialuminaire.com
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This is perhaps pedantic, but . . .

Mathematica is a rules engine. When it evaluates an input, it applies all the rules it has, until it reaches an expression to which no further rules apply. Then it returns that result.  These rules are the total of those built in and those you have added during the session by making assignments. For example Sin(x) is defined, where x is a number, by a built in rule. If you ask for Sin(3), you will get a numerical answer. But if you ask for Sin(x), where x is not defined, then it will return Sin(x). It can't evaluate this further because it does not have a numerical value for x. So it returns the fully evaluated answer, which is still Sin(x). However, if you had earlier made the assignment x=3, then it would also have a transformation rule for x. Applying that to Sin(X) gives Sin(3), and then it's built in rule is applied to give a numerical value.

In the case of Sin(3,2), there is no rule which applies. Mathematicas rules understand which arguments types are proper, and it has no rule called Sin which accepts two arguments, so it returns Sin(3,2). There is no rule to tranform the input. You will at times see this in functions you define. If you define foo(x_):=x, and then input foo(2,3), it will return foo(2,3).

NOTE THAT I INCORRECTLY USE () FOR ARGUMENTS BECAUSE THIS EDITOR STRIPS SQUARE BRACKETS.

Best regards,
David

When the Mathematica kernel cannot find an answer to what you want to evaluate, it will simply return the input.
This can also occur when the function you are using is undefined:For your case I'd guess that Minimize does not have any algorithm to solve your system for general h.
For given values of h NMinimize might work.