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. b=(d-c)/a
Step-by-step explanation:
make me a brainlist
The vertex to the equation is, (4,2)
Answer: the eastbound train had travelled 12 miles
Explanation: using Pythagoras theorem, we know that
X^2 = a^2 + b^2
Where ^ stands for raised to power.
Let
a stand for the train going towards North and
b stands for the train going towards east.
X stands for the total distance between train a and b = 20 miles.
By Pythagoras rule
X^2 = a^2 + b^2
20^2 = 16^2 + b^2
400 = 256 + b^2 so that
b^2 = 400 - 256 = 144
b = √144
b = 12 miles.
Answer:
225 students scored 65 or better and 75 students scored 88 or better.
Step-by-step explanation:
We are given that The five-number summary for the scores of 300 nursing students are given :
Minimum = 40

Median = 82

Maximum = 100
is the first quartile and is the median of the lower half of the data set. 25% of the numbers in the data set lie below
and about 75% lie above
.
is the third quartile and is the median of the upper half of the data set. 75% of the numbers in the data set lie below
and about 25% lie above 
i) .About how many students scored 65 or better?

Since we know that 75% lie above
.
So, Number of students scored 65 or better = 
ii)About how many students scored 88 or better?

Since we know that 25% lie above
So, Number of students scored 88 or better = 
Hence 225 students scored 65 or better and 75 students scored 88 or better.