Answer:
The fifth degree Taylor polynomial of g(x) is increasing around x=-1
Step-by-step explanation:
Yes, you can do the derivative of the fifth degree Taylor polynomial, but notice that its derivative evaluated at x =-1 will give zero for all its terms except for the one of first order, so the calculation becomes simple:

and when you do its derivative:
1) the constant term renders zero,
2) the following term (term of order 1, the linear term) renders:
since the derivative of (x+1) is one,
3) all other terms will keep at least one factor (x+1) in their derivative, and this evaluated at x = -1 will render zero
Therefore, the only term that would give you something different from zero once evaluated at x = -1 is the derivative of that linear term. and that only non-zero term is:
as per the information given. Therefore, the function has derivative larger than zero, then it is increasing in the vicinity of x = -1
<em>Question:</em>
<em>Abraham has visited at least 50 countries; he plans to visit five new countries per year (Y) for the next several years. Which inequality and solution shows the amount of years they will take for Abraham to meet his goal.</em>
Answer:


Step-by-step explanation:
Given
------ at least

Required
Represent as an inequality
"at least" means 
So the countries he has visited can be represented as thus;

If
1 year = 5 countries
y years would be 5y countries
So, in y years; he'd have visited

To determine the value of y.
We have that
<em>in the world</em>
<em>Substitute 195 for Countries</em>

<em>Collect Like Terms</em>


<em>Divide through by 5</em>


<em>Reorder</em>

This means that; he'll visit all countries in at most 29 years' time
Answer:
Rounding to the Nearest Integer
The most common type of rounding is to round to the nearest integer. The rule for rounding is simple: look at the digits in the tenth's place (the first digit to the right of the decimal point).