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 at very bottom of picture above
if explanation need comment
11/1.
Hope this helps,
and I hope you have a productive day!
Answer:
20+4x
Step-by-step explanation:
Distributive property is quite easy to learn... its just multiplication in an easier form to visualize once you're used to using it.
To first start this problem you want to use the number 4 in the expression 4(5+x). You then want to multiply 4 by both terms inside of the parentheses. So you would do both 4*5 and 4*x. You would then get 20+4x because 4*5=20 and 4*x is just put together as 4x.
Determine the base of right triangle by using pythagoras theorem.
![\begin{gathered} b=\sqrt[]{(15.7)^2-(8.5)^2} \\ =\sqrt[]{174.24} \\ =13.2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20b%3D%5Csqrt%5B%5D%7B%2815.7%29%5E2-%288.5%29%5E2%7D%20%5C%5C%20%3D%5Csqrt%5B%5D%7B174.24%7D%20%5C%5C%20%3D13.2%20%5Cend%7Bgathered%7D)
Determine the area of base of figure.
Determine the volume of the figure.
So volume of the figure is 347.82 yards square.
