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
ser-zykov [4K]
3 years ago
9

Find the absolute maximum and absolute minimum values of f on the given interval.

Mathematics
1 answer:
kvasek [131]3 years ago
5 0

Answer:

absolute max= (4.243,18)

absolute min =(-1,-5.916)

absolute max=(pi/6, 2.598)

absolute min = (pi/2,0)

Step-by-step explanation:

a) f(t) = t\sqrt{36-t^2} \\

To find max and minima in the given interval let us take log and differentiate

log f(t) = log t + 0.5 log (36-t^2)\\Y(t) = log t + 0.5 log (36-t^2)

It is sufficient to find max or min of Y

y'(t) = \frac{1}{t} -\frac{t}{36-t^2} \\\\y'=0 gives\\36-t^2 -t^2 =0\\t^2 =18\\t = 4.243,-4.243

In the given interval only 4.243 lies

And we find this is maximum hence maximum at  (4.243,18)

Minimum value is only when x = -1 i.e. -5.916

b) f(t) = 2cost +sin 2t\\f'(t) = -2sint +2cos2t\\f"(t) = -2cost-4sin2t\\

Equate I derivative to 0

-2sint +1-2sin^2 t=0

sint = 1/2 only satisfies I quadrant.

So when t = pi/6 we have maximum

Minimum is absolute mini in the interval i.e. (pi/2,0)

You might be interested in
How many solutions exist for the given equation? StartFraction one-half left-parenthesis x plus 12 right-parenthesis equals 4 x
Firlakuza [10]

Answer:

One solution x = 2

Step-by-step explanation:

Given the equation:

\dfrac{1}{2}(x+12)=4x-1

Multiply this equation by 2:

2\cdot \dfrac{1}{2}(x+12)=2\cdot (4x-1)\\ \\x+12=2(4x-1)

Use distributive property:

x+12=8x-2

Combine the like terms:

x+12=8x-2\\ \\x+12-12=8x-2-12\\ \\x=8x-14\\ \\x-8x=8x-14-8x\\ \\-7x=-14\\ \\7x=14\\ \\x=2

Thus, this equation has one solution x = 2

7 0
3 years ago
Read 3 more answers
Find all numbers whose absolute value is 3 . If there is more than one, separate them with commas. If there are no such numbers,
adelina 88 [10]

Answer:

3, and -3

Step-by-step explanation:

Because absolute value is the distance away from zero, |3| and |-3| would both be 3 units away from 0. Be sure to have the negative on the inside if you're trying to make something positive, otherwise -|3| means that the absolute value of 3 would then become negative since the negative sign isn't a part of the absolute. hope this helps!

3 0
3 years ago
Production increased from 8,200 units to 13,530 units; the percent increase was what?
mamaluj [8]
(13530-8200)/8200 times 100
6 0
3 years ago
Solve the equation. -0.2(30) + 0.5x = 0.2(30 + x)
Travka [436]

Answer:

x=40

Step-by-step explanation:

4 0
3 years ago
What are the solutions of the equation ( X -25 )^ 2 equals 36
fgiga [73]

Answer:

x = 31, x = 19

Step-by-step explanation:

(x-25)^2=36\\\sqrt{(x-25)^2}=\sqrt{36}\\x-25=6 or -6\\\\x-25=6\\x=31\\\\x-25=-6\\x=19

5 0
3 years ago
Other questions:
  • The standard deviation of the sampling distribution of the sample mean is $115,000. The population standard deviation was $25,00
    9·1 answer
  • Please plis help me with this equation is for tomorrow put with resolution plis which are in parentheses and written: "squared"
    13·1 answer
  • Assume the $12,000 Treasury bill, 3% for 13 weeks. Calculate the effective rate of interest
    15·1 answer
  • A car enters a turnpike 22 miles north of a town. The car teavels north at an average speed of 64 miles per hour. How far is the
    11·2 answers
  • PLEASE HELP!!! DUE TODAY
    10·1 answer
  • 4x-2=3 (x-1) Help solve this
    7·1 answer
  • Which ordered pair is a solution of the equation?<br> y = -3.2 – 4
    10·1 answer
  • ⚠WILL GET BRAINLEST...THE QUESTION IS AT THE BOTTOM ⚠How many solutions does have? O A. Two solutions B. No solutions C. Infinit
    8·1 answer
  • AHIJ has coordinates H(0, 0), I(-3, -1), and J-1, -2). Graph the triangle and its translation 3 units to the right and 2 units d
    7·1 answer
  • Liam says -() is equivalent to 2. Explain if Liam is correct by completing the
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!