find the derivative:
This is one of my homework problems and It says simplify the result
is sufficient, or should I factor out the x as well?
I'd like more than one opinion guys.
Questions that ask that (simplify the result) might as well also ask how long a piece of string is ....
The fact is that different people will have a different idea of what simplify the result means ....
However, since the basic answer can pretty much be written down by inspection in one line, I suspect the writer of the question wants you to factorise the answer. In which case, s/he should have just said to give your answer in factorised form.
Personally I find the use of broad instructions such as "simplify your answer" and their ilk ridiculous in many cases. In your case, I would have thought that the intent of the question was to test a basic skill (use of product rule), that the question would be worth 1 mark and that your answer would be sufficient. In which case, the instruction to "simplify the result" is even more ridiculous since potentially a student could get zero even though s/he has succesfully applied the skill.
Such instructions are especially potentially ridiculous in on-line tests. In my opinion, such a broad instruction usually makes the person who wrote the question look like a fool.
Instructions I typically use include:
".... and completely factorise your answer."
"Express your answer in exact surd form."
"Find in exact form ...."
"Find in the form where a, b and c are whole numbers ...."
"Find in the form y = mx + c the equation of the line ...."
etc.
In other words, I specifically prescibe the form I want the answer in.
I've been thinking that the whole time. When my professor says "simplfy the result", contextually, this can mean a number of things. Also, he himself has shown many different examples of what "simplify" means, which makes this statement all the more confounding. I believe, however, by my own personal intuition, that leaving this result as it is, because there is nothing that will come of the answer. If I was going to try and find where the function had any critical points, factoring would then be appropriate. Am I right?
p.s. I attend community college. My professor is by no means ivy elite.