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dem82 [27]
3 years ago
11

A theorem states that if f is continuous on an interval I that contains one local extremum at c and if a local minimum occurs at

c, then f(c) is the absolute minimum of f on I, and if a local maximum occurs at c, then f(c) is the absolute maximum of f on I. Verify that the following function satisfies the conditions of this theorem on its domain. Then, find the location and value of the absolute extremum guaranteed by the theorem.
f(x)= -xe^-x/4 The function f(x) = -xe^-x/4 has an absolute extremum of Q at x=.?
Mathematics
1 answer:
Artist 52 [7]3 years ago
3 0

Answer:

Step-by-step explanation:

To find the extremum of the function, you need to take the first derivative.f'(x) = (-x)'e^{-x/4} + (-x) (e^{-x/4})'

= e^{-x/4}(\frac{x-4}{4} )

This derivative = 0 if and only if x - 4 = 0, hence the extremum is at x = 4

To consider if it is local max or min, you need to consider the act of the function before and after x = 4 by making a table.

-\infty                                        4                                       +\infty

f(x)                 -                       0                +

                     \searrow                                         \nearrow

Hence x =4 is a  local min.

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KonstantinChe [14]

Answer:

5.20  to the nearest hundredth.

Step-by-step explanation:

The altitude line bisects the base of the triangle to form 2 right  angled triangles with hypotenuse = 6 and the base = 3.

So,  by the Pythagoras theorem the altitude is  calculated as follows:

6^2 = 3^2 + x^2

x^2 = 36 - 9 = 27

x = √27

= 5.20  to the nearest hundredth.

7 0
3 years ago
If janice plays a game once and the probability of getting yellow is 0.24. How many times will the color shown be yellow if she
blsea [12.9K]

Answer: 12

Step-by-step explanation:

Given

The probability of getting yellow color is 0.24

If the no of trials is 50

\text{No. of times yellow color shown(N) is}=p\times \text{no of trails}\\\Rightarrow N=0.24\times 50=12\ \text{times}

Yellow color appears 12 times

3 0
3 years ago
2. A large fruit-eating bat called the black flying fox, Pteropus alecto, occupies a large mangrove swamp on Indooroopilly Islan
Svetach [21]

Step-by-step explanation:

a. P(mites OR ticks) = P(mites) + P(ticks) − P(mites AND ticks)

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b. P(no ticks | mites) = P(no ticks AND mites) / P(mites)

P(no ticks | mites) = (0.80 − 0.20) / 0.80

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P(mites AND ticks) = 0.20

P(mites) × P(ticks) = 0.80 × 0.30 = 0.24

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3 years ago
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2 years ago
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mixas84 [53]

Answer: B: Independent, because the outcome of the first roll doesn't affect the outcome of the second roll.

Step-by-step explanation:

Events are independent when the outcome of one does not effect the other. Rolling dice for example: If you roll an even number on your first cube, there is no way that it will effect the roll on the second cube, hence the two events are independent.

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2 years ago
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