Part A. You have the correct first and second derivative.
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Part B. You'll need to be more specific. What I would do is show how the quantity (-2x+1)^4 is always nonnegative. This is because x^4 = (x^2)^2 is always nonnegative. So (-2x+1)^4 >= 0. The coefficient -10a is either positive or negative depending on the value of 'a'. If a > 0, then -10a is negative. Making h ' (x) negative. So in this case, h(x) is monotonically decreasing always. On the flip side, if a < 0, then h ' (x) is monotonically increasing as h ' (x) is positive.
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Part C. What this is saying is basically "if we change 'a' and/or 'b', then the extrema will NOT change". So is that the case? Let's find out
To find the relative extrema, aka local extrema, we plug in h ' (x) = 0
h ' (x) = -10a(-2x+1)^4
0 = -10a(-2x+1)^4
so either
-10a = 0 or (-2x+1)^4 = 0
The first part is all we care about. Solving for 'a' gets us a = 0.
But there's a problem. It's clearly stated that 'a' is nonzero. So in any other case, the value of 'a' doesn't lead to altering the path in terms of finding the extrema. We'll focus on solving (-2x+1)^4 = 0 for x. Also, the parameter b is nowhere to be found in h ' (x) so that's out as well.
Answer:
Yes, you are correct.
Step-by-step explanation:









The two numbers are -18+ 2√(11) and -18 -2√(11).
-18+ 2√(11)+ [-18 -2√(11)]= -36
[-18+ 2√(11)]* [-18 -2√(11)]= 280.
Hope this helps~
Solution: We are given:
Sales tax 
The pre-tax price of the supplies 
We have to find the total cost of the supplies.
We first need to find the sales tax on the price of supplies. The sales tax amount is:

Therefore, the total cost of the supplies = pre-tax price of the sales + sales tax amount
=$48 + $3.36
=$51.36
The answer is B.
The only reason it will be 200 is because the numbers 1,2,3,4,5,and 6 are all an option so the probability of 5 is 1/6 and if you multiply 1/6 by 1,200 you will get 200. Hope this helped!