Find all points of extrema on the interval [0,2pi] if y=x-cosx ...?

The function y=x-cosx has an extremum on the interval [0,2pi] at x=3pi/2, determined by setting the first derivative equal to zero. The second derivative test is inconclusive at this point, but the point (3pi/2, 3pi/2) is a minimum due to the nature of the function.

To find all points of extrema on the interval [0,2pi] for the function y=x-cosx, we first need to find the derivative of the function and determine where it is equal to zero. The first derivative of y=x-cosx is y' = 1 + sinx. The critical points occur where y' = 0, which translates to 1 + sinx = 0 or sinx = -1. The only point in the interval [0,2pi] where sinx = -1 is at x = 3pi/2. To determine if this critical point is a maximum or minimum, we apply the second derivative test.

The second derivative of the function is y'' = cosx. At x = 3pi/2, the second derivative y'' = cos(3pi/2) = 0; since the second derivative is zero, the second derivative test is inconclusive. However, we can analyze the function around the critical point to conclude or use other methods like analyzing the first derivative's sign change.

For y=x-cosx, since the original function is a combination of a linear increasing function and cosine function, the critical point at x = 3pi/2 will be a minimum as the function increases both before and after this point.

Therefore, the point of extrema on the interval [0,2pi] for the function y=x-cosx are at (3pi/2, 3pi/2 - cos(3pi/2)), which simplifies to (3pi/2, 3pi/2).

mBAC = 22.21°
mABC = 137.67°
mBCA = 20.12°

Classify the triangle by its angles

When the function below is graphed, how many x-intercepts does it have? y = 2x2 - 8x + 5

please helpppppp!!!!!

How far does the first car will drive in the 2 hours head start it gets? Now, at t = 2 hours, both cars are moving. How much faster is the second car than the first car? You can determine this by dividing the head start by the difference in the two speeds. If car 1 has a 20-mile head start, and car two is five mph faster, then it will take 20/5 = 4 hours to catch up.

Find tan θ if sec θ = (sqrt26)/5 and sin θ < 0.

Solve the problem. Round to the nearest hundredth of a percent if needed. During clinical trials of a new drug intended to reduce the risk of heart attack, the following data indicate the occurrence of adverse reactions among 1100 adult male trial members. What is the probability that an adult male using the drug will experience nausea?


A. 2.02%

B. 1.73%

C. 27.59%

D. 2.18%

describe how to draw a line that passes through the origin and has a slope of 3/5

Each of the 25 student in mr mcdounld class sold 16 tickets if each ticket costs15$ how much money did the students raise

Which statement is an example of the Identity Property of Multiplication?
8 • 0 = 0
8 • 1 = 8
8 • –1 = –8
–8 • –1 = 8

which of the following functions is graphed below??

A model is made of a car. The car is 8 FEET long and the model is 10 INCHES long. What is the ratio of the length of the car to the length of the model? a)10:8 b)48:5 c)5:48 d)8:10

Factor 5x^3 40x^2 - 100x

Find the sum of 86, 331, and 909.

Simplify the expression

sin(pi+x) + sin(pi - x)
...?

Write 6 ×10000 5×1000 2×100 3×1 as a number.

Each ratio in simplest form 16:40

Your class is selling boxes of flower seeds as a fundraiser. The total profit p depends on the amount x that your class charges for each box of seeds. The equation p equals negative 0.5 x squared plus 36 x minus 141p=−0.5x 2+36x−141 models the profit of the fundraiser.​ What's the smallest​ amount in​ dollars that you can charge and make a profit of at least ​$471​?

True or False?
(a^4)(a^5) = (a)^9

explain the difference between 1/(sinx) and ((sin^-1)x) ...?

Solve the equation

x^2 + 5x + 4 = 0

How do you solve (a^3b)^4(ab^6)^2?

Find the measures of two angles, one positive and one negative, that are coterminal with pi divided by five. How do you do this? :/

If segment UV is considered to be the base of parallelogram TUVW, which segment would represent the altitude of the parallelogram?

segment TU

segment TX

segment WT

segment WV

PLEASE HELP ...?

B is the midpoint of AC. Solve for the length of AB if AB=5x+3 and BC=7x+9

Jose has had his eye on a pair of basketball shoes at a shoe store for a long time, but at a price of $150, the shoes have always been a little bit more than his budget could handle. However, today he saw a sign in the window that said, "Basketball Shoes – 20% off." Which type of discount is this?

A. A sale
B. A coupon
C. A rebate
D. A gift card

Eugenia wants to find out how fast she walked along the hiking trail that took her 1.5 h to complete. She counted the number of steps with a pedometer and got 10000 steps. in order to calculate the distance she walked she estimated the length of her stride. she walked 10 steps three times at her usual rate and measured the distance with a measuring tape (the smallest division is 1cm) and got 745cm, 748 cm, 739 cm. Find the length of her stride. What is the length of the hiking trail? What are absolute and relative uncertainties in that length?

how do you find the equation of a triangles altitude using point slope formula?

A candy company used 8 gallons of syrup to make 4 batches of candy. what is the rate of syrup per batch.

Divide 28x3 + 42x2 - 35x by 7x

The maximum gas mileage for a compact car is estimated using the graph shown below.


The average gas mileage for an SUV is modeled by the function m(s)=−0.015(s−55)2+15, where s is the SUV's speed in miles per hour.


The difference in maximum mileage between these two vehicles is _____ mpg (miles per gallon).


Enter the number that correctly fills in the blank in the previous sentence.

write an equation in point slope form for the line through the given point with the given slope
(8,3) m =5
A. Y+3=5(x-8)
B. Y+3=5x-8
C.y-3=5(x-8)
D.y-3=5(x+8)