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:5
Explaining:
10% of 50
= 10%=10/100 = 0.1
= 0.1 (x) times 50
= 5
<h3>
Answer: 3. Postulate</h3>
A postulate is something that is assumed to be true and there isn't a proof for it as its something foundational to help set up further proofs later down the road. Another example of a postulate is that a line is defined by two distinct points.
Answer:
The answer is below
Step-by-step explanation:
The question is not complete. But I would show you how to solve the problem.
Two events A and B are said to be independent if the occurrence of event A does not affect the occurrence of event B and vice versa. P(A and B) = P(A) * P(B).
Two events A and B are said to be mutually exclusive if event A and event B cannot occur at the same time. P(A and B) = 0.
Two events A and B are said to be complementary when event A occurs if and only if event B does not occur and vice versa.
