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:
1.) 1-b, 2-a, 3-d, 4-c
Step-by-step explanation:
You recognize that the point-slope form of the equation for a line with slope m and point (h, k) is ...
... y - k = m(x - h)
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Match this form to the given equations to determine (h, k). Once you determine (h, k) from the equation, find that point in the list of points to get your match-up. (All the slopes are correct, so you don't need to do any more work than just described.)
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For problems 3.) and 4.), use the above form with the given point and slope.
Step-by-step explanation:
Question 1)
Given
The expression is 5xy
To determine
Find the value of 5xy if x = 2 and y = 3
5xy
substitute x = 2 and y = 3
5xy = 5(2)(3)
= 5(6)
= 30
Therefore, the value of 5xy = 30 if x = 2 and y = 3.
<em>Note: your remaining questions are not mentioned. But, the procedure may remain the same. Hopefully, your concept will be cleared anyway.</em>
Answer:
False
Step-by-step explanation:
It is given that Noah thinks :
9x - 2x + 4x = 3x as the subtraction sign after 9x tells us to subtract everything that comes after 9x.
This is wrong as according to the BODMAS rule, we have to do the addition operation first and then followed by subtraction operation.
That is
⇒ 9x - 2x + 4x
⇒ (9x -2x)+ 4x
⇒ 7x + 4x
⇒ 11x
Therefore the answer to the equation is 11x and not 3x.
