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.
Let
x--------> the number of blue beads
y--------> the number of red beads
we know that
-------> equation 
------> equation 
equate equation and equation
find the value of x
therefore
the answer is
Ivan has 
We need to get x alone, to do that we add 1 to both sides to cancel out the -1 on the right.
-4 = x -1
+1 +1
-3=x
This means x is equal to -3. Hope this helps!
We know that
[volume of a <span>regular hexagonal prism]=[area of the base]*height
height=volume/area of the base
h=160/64-----> 2.5 m
[surface area </span><span>hexagonal prism]=2*[area of the base]+[perimeter of base]*h
</span>[surface area hexagonal prism]=2*[64]+[30]*2.5----> 203 m²
the answer is
203 m²
