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gogolik [260]
3 years ago
14

Consider the function on the interval (0, 2π). f(x) = sin(x) cos(x) + 8 (a) Find the open interval(s) on which the function is i

ncreasing or decreasing. (Enter your answers using interval notation.) increasing decreasing (b) Apply the First Derivative Test to identify all relative extrema. relative maxima (x, y) = (smaller x-value) (x, y) = (larger x-value) relative minima (x, y) = (smaller x-value) (x, y) = (larger x-value)
Mathematics
1 answer:
makkiz [27]3 years ago
7 0

Answer:

a) Increasing in

(0,\frac{\pi}{4})

(\frac{5\pi}{4},2\pi)

decreasing

(\frac{\pi}{4},\frac{5\pi}{4})

Local maximum

\frac{\pi}{4}

Local minimum

\frac{5\pi}{4}

Step-by-step explanation:

Let f(x) be

f(x) = sin(x)+cos(x)+0 for 0<x<2π.

Taking the first derivative

f'(x) = cos(x)-sin(x)

The critical points are those where the derivative vanishes.

f'(x) = 0 iif cos(x) = sin (x), so, the critical points in (0, 2π) are

x=\frac{\pi}{4}\;and\; \frac{5\pi}{4}

To find out what kind of critical points they are, we take the second derivative

f''(x) = -sin(x)-cos(x)

Evaluate this expression at the critical points

f''(\frac{\pi}{4})=-\frac{\sqrt2}{2}-\frac{\sqrt2}{2}< 0

so, this point is a local maximum.

f''(\frac{5\pi}{4})=\frac{\sqrt2}{2}+\frac{\sqrt2}{2}> 0

and here we have a local minimum.

The function then is increasing in the intervals

(0,\frac{\pi}{4})\;and\;(\frac{5\pi}{4},2\pi)

and decreasing in

(\frac{\pi}{4},\frac{5\pi}{4})

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Answer: D) Increase the sample size and decrease the confidence level.

Step-by-step explanation:

A reduced interval width means that the data is more accurate. This can only be achieved if the sample size is increased because a larger sample size is able to capture more of the characteristics of the variables being tested.

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8 0
3 years ago
A jacket cost $35.50 more than a pair of tennis shoes if the total cost of both items is $161.30 find the cost of each
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Answer:

$62.9 and $98.4

Step-by-step explanation:

Let the cost of tennis shoe be x

Since a jacket cost $35.50 more than a pair of tennis shoe,

Then cost of jacket would be

= $35.50 + x

Total cost of both items would be;

x + $35.50 + x = $161.30

2x = $161.30 - $35.50

2x = $125.8

x = $62.9

Therefore, cost of pair of tennis shoe is $62.9

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6 0
3 years ago
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Find three consecutive integers whose sum is 57????
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Answer:18 19 20

Step-by-step explanation:"Consecutive"  means that the integers will follow each other in value, for example:  1, 2, 3 or 4, 5, 6.  Also, no decimals are needed here because "integers" are whole, counting numbers. Here is the set up:   Let x= the first integer     Then    X+1= 2nd consecutive integer   and x+2= 3rd  .  

Suppose that x=1   x+1= 1+1=2   and x+2=1+2=3   However, you need specific consecutive numbers whose sum is 57.  Remember that sum means to add:

x+  (x+1)  + (x+2) = 57                 Addition of all 3 consecutive numbers   Now solve for x

                                                   and substitute into each part to come up with the three integers:

3x + 3= 57        3x=54               x=54/3  =  18            x=18,   x+1= 18+1=19      x+2=18+2=20

Check your answer:  18+19+20=57                 57=57  Check

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