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lapo4ka [179]
2 years ago
13

Determine the location and absolute maximum and absolute minimum for the given function f(x)=(_x+2)^4 where 0

Mathematics
1 answer:
ELEN [110]2 years ago
6 0

Answer:

the minimum is 0 and the maximum is 16.

Step-by-step explanation:

For a function f(x), the maximum is defined as:

f(xₐ)

such that:

f(xₐ) ≥ f(x) for every value of x in the domain.

And the minimum is:

f(xₙ)

Such that:

f(xₙ) ≤ f(x)

for every value of x.

Now, in this case we have the function:

f(x) = (-x + 2)^4 in the range  0 < x < 3

First, let's analyze our function.

We can see that the exponent is even, then:

f(x) = (-x + 2)^4

Can be equal to zero or larger than zero.

Then the minimum will be f(x) = 0

To find this, we need to find the value of x such that:

-x +2 = 0

2 = x

Then the minimum is:

f(2) = (-2 + 2)^4 = 0

For the maximum, we can just play with the other values in the range and see which one gives the larger value of f(x).

Again, because f(x) =  (-x + 2)^4 , the maximum will be at the value of x such that:

|-x + 2| is maximized.

As we have a negative sign multiplying x, the smaller value in the range:

x = 0

is the one that maximizes that:

|-0 + 2| = |2| = 2

Evaluating f(x) in x = 0 we get:

f(0) = (0 + 2)^4 = 16

Then the minimum is 0 and the maximum is 16.

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the answer is 70% your welcome

4 0
3 years ago
You invested money in two funds. Last year, the first fund paid a dividend of 8% and the second a dividend of 5%, and you receiv
Angelina_Jolie [31]

You invested 11000 in in 2st fund and 9000 in 2nd fund

<h3><u>Solution:</u></h3>

Given that, You invested money in two funds.  

Last year, the first fund paid a dividend of 8% and the second a dividend of 5%, and you received a total of $1330.  

This year, the first fund paid a 12% dividend and the second only 2%, and you received a total of $1500.

Let the amount in Fund I be $x and amount in Fund II be $ y

Then, for last year ⇒ 0.08x+0.05y=1330 ----- eqn (1)  

And for this year ⇒ 0.12x+0.02y=1500 ------- eqn (2)  

Multiply (1) by 2 ⇒ 0.16 x + 0.1 y = 2660  

Multiply (2) by 5 ⇒ 0.6 x + 0.1 y = 7500

Subtract the two equations  

(2) ⇒ 0.6x + 0.1y = 7500

(1) ⇒ 0.16x + 0.1y = 2660

(-) --------------------------------

0.44x + 0 = 4840

x = 11000

Now, from eqn (2)  

0.12(11000) + 0.02y = 1500  

0.02y = 1500 – 1320  

0.02y = 180  

y = 9000

Hence, he invested 11000 in in 2st fund and 9000 in 2nd fund

5 0
3 years ago
Lf f(x) = 5x, what is f^-1(x)?
Nonamiya [84]

Answer: f^{-1}(x)=\frac{x}{5}

Step-by-step explanation:

By definition the domain of an inverse function f^-1(x) is the range of f(x) and the range of the inverse function is equal to the domain of the principal function f(x).

If you have a function f(x)=5x, then to find the inverse function, follow these steps:

1. Make y=f(x)

 f(x)=y=5x

 y=5x

2. Solve for the variable "x":

x=\frac{y}{5}

3. Exchange the variable "x" with the variable "y":

y=\frac{x}{5}

4. Exchange "y" withf^{-1}(x). Then the inverse function is:

f^{-1}(x)=\frac{x}{5}

7 0
3 years ago
I don’t get this answer
matrenka [14]

23 units sure does hope this helps


3 0
3 years ago
A line has an x-intercept of 4 and a y-intercept of -2. What is the equation of the line?
Evgesh-ka [11]

Answer:

y=x/2-2

Step-by-step explanation:

it's actually 1/2 times x is how your supposed to write it (like a fraction)

7 0
3 years ago
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