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Brut [27]
3 years ago
9

Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 − 9x2 − 108x + 6, [−3, 4]

Mathematics
2 answers:
Leni [432]3 years ago
8 0

Answer:

The absolute maximum of f(x) on [-3, 4] is 138 and the absolute minimum of f(x) on [-3, 4] is -237.

Step-by-step explanation:

To find the absolute extrema values of f(x) = 6x^3 - 9x^2 - 108x + 6  on the closed interval [−3, 4] you must:

1. Locate all critical values. We need to find the derivative of the function and set it equal to zero.

\frac{d}{dx}f(x)= \frac{d}{dx}\left(6x^3-9x^2-108x+6\right)=\\\\f'(x)=\frac{d}{dx}\left(6x^3\right)-\frac{d}{dx}\left(9x^2\right)-\frac{d}{dx}\left(108x\right)+\frac{d}{dx}\left(6\right)\\\\f'(x)=18x^2-18x-108

18x^2-18x-108=0\\18\left(x^2-x-6\right)=0\\18\left(x+2\right)\left(x-3\right)=0\\\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=-2,\:x=3

2. Evaluate f(x) at all the critical values and also at the two values -3 and 4

\left\begin{array}{cc}x&f(x)\\-3&87\\-2&138\\3&-237\\4&-186\end{array}\right

3. The absolute maximum of f(x) on [-3, 4] will be the largest number found in Step 2, while the absolute minimum of f(x) on [-3, 4] will be the smallest number found in Step 2.

Therefore,

The absolute maximum of f(x) on [-3, 4] is 138 and the absolute minimum of f(x) on [-3, 4] is -237.

Alborosie3 years ago
5 0
It is convenient to use a graphing calculator for this. The graph shows the maximum and minimum are not at the ends of the interval, so could be found by differentiating the function and setting that derivative to zero. The function would then need to be evaluated for those solutions {-2, 3}.

The absolute minimum on the interval is -237 at x=3.
The absolute maximum on the interval is 138 at x=-2.

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Ellen flipped a coin 80 times. the coin landed heads up 44 times and tails up 36 times. what is the theoretical probability of l
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Answer:

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5 0
3 years ago
What is 0.7, 0.755, 5/8 from least to greatest?
Margarita [4]
I like to start by turning all my numbers into the same form.  You can go either way but I am going to turn the decimals into fractions.  so 0.7 is the same as 7/10.

0.755 is like 755/1000 which can be reduced to 151/200  (if you don't understand the convertions let me know i will explaine more.)

Next give all the fractions a common denominator. both 8 and 10 go into 200 so we can use that.  151/200 already has a denominator of 200 so that one is set.
for 7/10  well, 10 time 20 is 200 so multiply both the numerator and the denominator by 20 so you get 140/200
the last one is 5/8  8 times 25 is 200 so multiply both numbers by 25 to get 125/200  

the fractionos we have are 125/200  151/200 and 140/200.  Now because they all have the same denominator the one with the lowest numerator is the least number and the one with the highest number is the greatest number.

125/200  140/200  151/200  now just replace the original number with the order they are placed in.
125/200 was 5/8
140/200 was 0.7 
151/200 was 0.755
so the final answer is 
5/8, 0.7, 0.755
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3 years ago
Wich tool is used to measure the lengths of segments when preforming a formal geometric construction
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A ruler as that is the only option that can measure segments

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Charles needs construction paper to finish a project. To wrap the box he knows he needs a lot of construction paper. The box is
san4es73 [151]

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3 years ago
HELP ASAP PLSSSSSSSSSS
inysia [295]

Answer:

Neighborhood Q appears to have a bigger family size

Step-by-step explanation:

Mean = the sum of all data values divided by the total number of data values

Number of families in Neighborhood Q = 9

Mean family size of Neighborhood Q:

= (2 + 5 + 4 + 3 + 2 + 5 + 3 + 6 + 5) ÷ 9

= 35 ÷ 9

= 3.888888...

Number of families in Neighborhood S = 9

Mean family size of Neighborhood S:

= (2 + 3 + 2 + 3 + 7 + 2 + 3 + 3 + 2) ÷ 9

= 27 ÷ 9

= 3

The mean family size of Neighborhood Q is 3.88..  and the mean family size of Neighborhood S is 3.  Therefore, Neighborhood Q appears to have a bigger family size as it's average family size is bigger than that of Neighborhood S.

6 0
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