Answer:
y = √(x - 3)
Step-by-step explanation:
The graph shown has exactly the same shape as does the graph of y = √x, EXCEPT that the entire graph of y = √x has been translated 3 units to the right. Thus, the function describing this graph is y = √(x - 3).
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. 210 meters per second .
2. 756 kilometers per hour.
Step-by-step explanation:
Given : The formula 
to calculate the estimated speed, in meters per second of a tsunami.
1. If the disturbance occurred at an ocean depth of 4,500 meters.
Then put d= 4500 in the above formula , we get
Hence, if the disturbance occurred at an ocean depth of 4,500 meters , the estimated speed would be 210 meters per second .
Also, A meter per second is equal to 3.6 kilometers per hour.
i.e. 1 meter per second = 3.6 kilometers per hour
Then by unitary method ,
210 meters per second =
kilometers per hour
=756 kilometers per hour.
