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:
<em>L = 24,873.6 miles</em>
Step-by-step explanation:
<u>Length of the Circumference</u>
Given a circle of radius r, the length of the circumference, or line surrounding the shape is:
The Earth has a diameter of 7,917.5 miles. The radius is half the diameter:
r=7,917.5/2=3,958.75 miles
Assuming a plane flies around the equator at ground level, the distance it would travel is:
L = 24,873.6 miles
Answer: 2.815 kilograms
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Work Shown:
1 layer = 0.5 kg
5 layers = 5*(0.5 kg) = 2.5 kg
icing = 15 g = 15/1000 = 0.015 kg
1 candle = 100 g = 100/1000 = 0.1 kg
3 candles = 3*(0.1 kg) = 0.3 kg
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The five layers combine to 2.5 kg. On top of that we have 0.015 kg of icing, and then finally the three candles add 0.3 kg more weight.
The total weight is therefore: 2.5+0.015+0.3 = 2.815 kilograms
Answer:
Step-by-step explanation:
The square indicates that the total angle is 90 degrees so
d+59=90
d=90-59
d=31 degrees
Although there is no picture, I will assume this is a triangle we are talking about since the terms base and height are being used. If that is the case, the height is roughly 38.72in.
To find this, we will use the area of a triangle formula.
1/2bh = a ---> plug in known values.
1/2(12.6)(h) = 244 ---> multiply to simplify
6.3(h) = 244 ----> divide both sides by 6.3
h = 38.73
