Answer:
A commercial site might have reliable information, you have to be extra careful because commercial sites promote businesses, products, or services, so the content is likely to be biased toward whatever is being promoted. Once you have looked at the overall website, look at who wrote the article you are interested in. The article should include the author’s name, qualifications, and contact information. Consider whether the author is an expert on the subject matter and whether the author is qualified to write about it.
Explanation:
(a)
We have been given an equation
. Upon taking derivative of this equation with respect to x on both the sides, we get:

(b)
In order to write the equation of tangent line, we need to find the slope of the line. We know that point (3,11) lies on the graph. Therefore, we write the slope of the tangent as:

Therefore, equation of tangent line is:

(c)
We know that slope of tangent is given as
. The tangent will be vertical when denominator of slope is zero, that is:

I belive the answer to the first one is no I would have to assume a habitual zone is one area on a planet. for example, an air conditioned building vs. the Savvanah dessert. However I am not sure maybe other answers will help more on this one. Sorry.... Earth-like planet would of course need water, plant life, animals, oxygen, fossil fuels etc. A challenge we would face on a travel to another liveable planet: do we have engough transportation? engough fuel to make it? How long can we live on this planet? Who or what else is present here? etc. Yes I do think they should discover a planet with earth like qualities befor investing in tools to get us to them. So money is not wasted. (make sure to put this into your own words )