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
meriva
3 years ago
12

Can relative maximums and minimums be at the endpoints? I know global max/min can be at endpoints but I'm not sure about relativ

e max/min.
Mathematics
1 answer:
KatRina [158]3 years ago
5 0

Answer:

No

Step-by-step explanation:

Just because the derivative is 0 at a point doesn't necessarily mean it is a relative minimum or maximum.  You must be able to evaluate the derivative on both sides of the point to determine if it changes signs.  Since endpoints have only one side, they cannot be relative maximums or minimums.

You might be interested in
7.9 - 4.012. I really don't know the answer
Lunna [17]
3.888 :))))))))))))))))))))))))))
7 0
3 years ago
A tank initially has 300 gallons of a solution that contains 50 lb. of dissolved salt. A brine solution with a concentration of
belka [17]

Let <em>s(t)</em> be the amount of salt in the tank at time <em>t</em>. Then <em>s(0)</em> = 50 lb.

Salt flows into the tank at a rate of

(2 gal/min) (6 lb/gal) = 12 lb/min

and flows out at a rate of

(2 gal/min) (<em>s(t)</em>/300 lb/gal) = <em>s(t)</em>/150 lb/min

so that the net rate at which salt is exchanged through the tank is

d<em>s(t)</em>/d<em>t</em> = 12 - <em>s(t)</em>/150 … (lb/min)

Solve for <em>s(t)</em>. The DE is separable, so we have

d<em>s</em>/d<em>t</em> = 12 - <em>s</em>/150

150 d<em>s</em>/d<em>t</em> = 1800 - <em>s</em>

150/(1800 - <em>s</em>) d<em>s</em> = d<em>t</em>

Integrate both sides to get

-150 ln|1800 - <em>s</em>| = <em>t</em> + <em>C</em>

Solve for <em>s</em> :

ln|1800 - <em>s</em>| = -<em>t</em>/150 + <em>C</em>

1800 - <em>s</em> = exp(-<em>t</em>/150 + <em>C </em>)

1800 - <em>s</em> = <em>C</em> exp(-<em>t</em>/150)

<em>s</em> = 1800 - <em>C</em> exp(-<em>t</em>/150)

Now given that <em>s(0)</em> = 50, we solve for <em>C</em> :

50 = 1800 - <em>C</em> exp(-0/150)

50 = 1800 - <em>C</em>

<em>C</em> = 1750

Then the amount of salt in the tank at any time <em>t</em> ≥ 0 is

<em>s(t)</em> = 1800 - 1750 exp(-<em>t</em>/150)

To find the time it takes for the tank to hold 100 lb of salt, solve for <em>t</em> in

100 = 1800 - 1750 exp(-<em>t</em>/150)

1700 = 1750 exp(-<em>t</em>/150)

34/35 = exp(-<em>t</em>/150)

ln(34/35) = -<em>t</em>/150

<em>t</em> = -150 ln(34/35) ≈ 4.348

So it would take approximately 4.348 minutes.

By the way, we didn't have to solve for <em>s(t)</em>, we could have instead stopped with

-150 ln|1800 - <em>s</em>| = <em>t</em> + <em>C</em>

Solve for <em>C</em> - this <em>C</em> <u>is not</u> the same as the one we found using the other method. <em>s(0)</em> = 50, so

-150 ln|1800 - 50| = 0 + <em>C</em>

<em>C</em> = -150 ln|1750|

==>   <em>t</em> = 150 ln(1750) - 150 ln|1800 - <em>s</em>|

Then <em>s(t)</em> = 100 lb when

<em>t</em> = 150 ln(1750) - 150 ln(1700)

<em>t</em> = 150 ln(1750/1700)

<em>t</em> = 150 ln(35/34)

<em>t</em> ≈ 4.348

5 0
3 years ago
Fihd the area of the triangle.<br> 6<br> 8<br> square units
damaskus [11]

Answer:

area of triangle is

\frac{1}{2} * b*h\\\\\frac{1}{2} *6*8\\\\6*4=24

7 0
2 years ago
A sock drawer has 17 folded pairs of socks, with 5 pairs of white, 8 pairs of black and 4 pairs of blue. What is the probability
jolli1 [7]

Answer:

26.4%

Step-by-step explanation:

PLS GIVE BRAINLIEST

8 0
3 years ago
Explain how using basic facts can help you find 10x20x30x40 mentally
kvv77 [185]
You just do 1x2x3x4
and then that equals 24
so now you have 24 and then you add 4 zeros because their are 4 zeros in the equation so then the final answer is
240000
8 0
3 years ago
Other questions:
  • 1.If 70% is £14, what is the full cost
    15·1 answer
  • Write the equation of a line that is perpendicular to the given line and that passes through the given point. y-4=5/2(x+3);(-3,4
    11·1 answer
  • Remi has $8.40 in a jar that contains only nickels and dimes. There are 108 coins in the jar. How many nickles are in the jar
    6·2 answers
  • Bell
    15·1 answer
  • Mr holins gives 800 dollars every month and it is only 16% of his buget how much is his whole buget
    6·1 answer
  • B) 3x+2 = 2x + 13 divided by 3
    9·1 answer
  • The circumference of the base of a cylinder is 24π mm. A similar cylinder has a base with circumference of 60π mm. The lateral a
    5·2 answers
  • inches? What is the side length of an equilateral triangle with a perimeter of 36 36% inches B 181 inches C121 inches D 122 inch
    15·1 answer
  • Question 4 Given: f(x) = -3x – 3 and g(x) = x2 + 5 Find (f - g) ().​
    5·1 answer
  • You have been working hard and saving money to buy your first used car - woo hoo! But you still need more money. (It's an expens
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!