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.
Since the average of 6 tests is 6, and we know that the average is found by dividing the total score by the number of tests, we can just multiply the average by the number of tests to find the total score. Doing this, we get 82 * 6 which simplifies to 492.
Answer:
No mode ???? I'm not sure
Answer: 24.84%
Step-by-step explanation:
I don't really know how to explain step-by-step from my messy notes
<span>To get the Least Common Multiple (LCM) of 37 and 12 we need to factor each value first and then we choose all the factors which appear in any column and multiply them:
<span><span>37: 37</span><span>12: 223 </span><span>LCM: 22337</span></span>The Least Common Multiple (LCM) is: 2 x 2 x 3 x 37 = 444</span><span> </span>
