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Grace [21]
3 years ago
6

Find the value of x at which the function has a possible relative maximum or minimum point.​ (Recall that e Superscript x is pos

itive for all​ x.) Use the second derivative to determine the nature of the function at these points.
f(x)=(3+x)e-4x

What is the value of x at which the function has a possible relative maximum or minimum point?

1a. Is the point a relative maximum or mininum?
Mathematics
1 answer:
shutvik [7]3 years ago
6 0

Answer:

x= -11/4 is a maximum.

Step-by-step explanation:

Remember that a function has its critical points where the derivative equal zero. Therefore we need to compute the derivative of this function and find the points where the derivative is zero. Using the chain rule and the product rule we get that

f'(x)=  -e^{-4x}(11+4x)

And then we get that   if   11+4x = 0   then   x = -11/4 . So it has a critical point at   x = -11/4.

Now, if the second derivative evaluated at that point is less than 0 then the point is a maximum and if is greater than zero the point is a minimum.

Since

f''(x) = 8e^{-4x} (5+2x)\\f''(-11/4) = -239496.56

x= -11/4 is a maximum.

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Graph is your answer look below for proof

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3 0
3 years ago
Help me with these 3 questions, please
Zina [86]

Answer:

1. x = -4y ---> y = (-1/4)x

slope = -1/4. y-intercept = (0,0)

2. y = -2x + 4

3. y = (1/3)x - 1

Step-by-step explanation:

1. Re-write your equation so that x is on the right and y is on the left:

x = -4y ---> y = (-1/4)x

slope = -1/4. y-intercept = (0,0)

2. y-intercept = (0,4) ----> P1

x-intercrpt = (2,0) ----> P2

slope m = (y2 - y1) / (x2 - x1)

= (0 - 4)/(2 - 0)

= -2

therefore, y - y1 = mx - x1 ---> y - 4 = -2x

or y = -2x + 4

3. y-intercept = (0,-1)

x-intercept = (3,0)

m = (0 - (-1)) / (3 -0) = 1/3

y - (-1) = (1/3)x - 0 ---> y = (1/3)x - 1

5 0
3 years ago
Which equation represents a population of 210 animals that decreases at an annual rate of 14%
soldi70 [24.7K]

Answer:

The equation i.e. used to denote the population after x years is:

P(x) = 490(1 + 0.200 to the power of x

Step-by-step explanation:

This problem could be modeled with the help of a exponential function.

The exponential function is given by:

P(x) = ab to the power of x

where a is the initial value.

and b=1+r where r is the rate of increase or decrease.

Here the initial population of the animals are given by: 490

i.e. a=490

Also, the rate of increase is: 20%

i.e. r=20%

i.e. r=0.20

Hence, the population function i.e. the population of the animals after x years is:

P(x) = 490(1 + 0.200 to the power of x

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Answer:

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Step-by-step explanation:

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The ratio of boys to girls is 5:3 there are 80 more boys than girls how many girls are there
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Answer: 120

<u>Step-by-step explanation:</u>

              Ratio      Quantity

Boys:        5           80 + x                  

Girls:         3              x

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5 0
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