1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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})

You might be interested in
Relationship between the value of the given digits 6s in 660
expeople1 [14]
We have the given number = 660
Now, explain the relationship of 6s in the given number.
=> 6 = hundreds
=> 6 = tens
=> 0 = ones
This is also another form:
=> 6 = 600
=> 6 = 60,
now, notice that the first value of 6 in the leftmost side is 10 times higher than the next number 6.
=> 60 x 10 = 600.
Thus, 600 is 10 times greater than 60 and vice versa.



5 0
3 years ago
Help mayyy pleaseee and tyy
Kay [80]

Answer:

2x=-7y not sure tho just guessping probably wrong sorry

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
If f(x) = |x|+ 9 and g(x) = -6, which describes the value of (f + g)(x)?
ohaa [14]

Answer:

(f+g)(x) > 3 for all values of x

4 0
3 years ago
What is (-4,-7) and (-6,9) in slope intercept form
quester [9]

Answer:

y = - 8x - 39

8 0
3 years ago
A car's speed is 45 miles per hour. How far will it go in 4 hours and 20 mins?
PIT_PIT [208]

Hi Quanzia25,

Solution:

45mph

45mph x 4hrs. = 180 miles in 4 hours

45 / 3 = 15

180 + 15 = 195

Answer:

The car has traveled 195 miles.

7 0
3 years ago
Read 2 more answers
Other questions:
  • The volume V of a fixed amount of a gas varies directly as the temperature T and inversely as the pressure P. Suppose that V=160
    14·1 answer
  • Select the best definitions of population and sample. A sample is the group from whom information is being collected. A populati
    6·1 answer
  • Help please !!!!!!!!!!!!!
    8·1 answer
  • Line GJ is tangent to point A at point G.<br><br> If AG = 9 and GJ = 12, find AJ.
    13·2 answers
  • What two numbers add up to -22 and multiply to -75
    5·1 answer
  • Before his trip to France, Shawn exchange $225 U.S. Dollars for euros at a rate of $1.35 U.S. Dollars to 1 euro. Determine the a
    12·1 answer
  • Pls help i cant find​
    6·2 answers
  • The box plot below describes a data set. Which of the following has a value of 18?
    14·2 answers
  • A large jar contains 500 marbles. All of the marbles in the jar are either blue or yellow, and there are 3 times as many blue ma
    8·1 answer
  • The sum of three consecutive odd integers. what are the three integers
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!