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2 years ago

For the polynomial function ƒ(x)= −2x2 − 4x + 16, find all local and global extrema.

Mathematics

1 answer:

rusak2 [61]2 years ago

7 0

For the given quadratic equation we only have a maximum at y = 18.

<h3>How to find the extrema of the given function?</h3>

Here we have:

$f(x) = -2x^2 - 4x + 16$

Notice that this is a quadratic equation of negative leading coefficient.

Then we have a maximum at the vertex, and both arms tend to negative infinity as x tends to infinity or negative infinity.

The vertex is at:

x = -(-4)/(2*(-2)) = -1

The maximum is:

$f(-1) = -2*(-1)^2 - 4*(-1) + 16 = -2 + 4 + 16 = 18$

If you want to learn more about quadratic equations:

brainly.com/question/1214333

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Bob Nale is the owner of Nale's Texaco GasTown. Bob would like to estimate the mean number of litres (L) of gasoline sold to his

Fudgin [204]

Answer:

The point estimate of the population mean is $\= x = 56$

The 80% confidence level is $50.57 < \mu < 61.43$

There is 80% confidence that the true population mean lies within the confidence interval.

Step-by-step explanation:

From the question we are told that

The sample size is n = 18

The standard deviation is $\sigma = 18 \ L$

The sample mean is $\= x = 56$

Generally the point estimate of the population mean is equivalent to the sample mean whose value is $\= x = 56$

Given that the confidence interval is 80% then the level of significance is mathematically represented as

$\alpha = 100 - 80$

$\alpha = 20 \%$

$\alpha = 0.20$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table

The value is $Z_{\frac{ \alpha }{2} } = 1.28$

Generally the margin of error is mathematically evaluated as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E = 1.28 * \frac{18 }{\sqrt{18} }$

=> $E = 5.43$

Generally the 80% confidence interval is mathematically represented as

$\= x - E < \mu < \= x + E$

=> $56 - 5.43 < \mu < 56 + 5.43$

=> $50.57 < \mu < 61.43$

The interpretation is that there is 80% confidence that the true population mean lies within the limit

3 0

3 years ago

Q23. Look at the image

alisha [4.7K]

Answer:

B. First term = 5, Common difference = -3

Step-by-step explanation:

The first term is f(1) = 8 - 3(1) = 8 - 3 = 5.

The common difference is the coefficient of n. Another way to see this is to compute the second term, f(2) = 8 - 3(2) = 8 - 6 = 2. The second term is 3 less than the first. The common difference is -3.

The sequence goes 5, 2, -1, -4, ...

4 0

3 years ago

A and b are positive integers and a−b=2. Evaluate the following: 3^b/3^a

Lerok [7]

Answer:

The answer is 1/9.

Step-by-step explanation:

Using the equation a-b=2, we can solve that a = 2+b.

We can then <u>substitute that into the expression</u> given to get 3^b/3^(2+b).

Since <u>they have the same base, we can subtract the exponents from the numerator and denominator</u> to get 3^(b-2-b) which <em>simplifies to 3^-2.</em>

3^-2 is simply 1/9.

8 0

3 years ago

Read 2 more answers

What is 2 1/4 x 3 1/2

Usimov [2.4K]

9.625 in decimals hope this helps

4 0

3 years ago

Read 2 more answers

Jimmy walked from his house, to school, then to the store, and finally back home. The distance from the school to the store

Blababa [14]

The distance from Jimmy's house to the school is 400 meters.

Step-by-step explanation:

Step 1; Assume that the distance between Jimmy's house and his school is x meters. So from the given data, we can form these

Distance from his house to the school = x,

Distance from his school to the store = Distance from his house to the school + 100 = x + 100,

Distance from the store to his house = Distance from his house to the school + 175 = x +175.

Step 2; It is given that the total distance Jimmy walked was 1,475 meters. Jimmy walked a total of three trips so,

x + x + 100 + x + 175 = 1,475,

3x + 275 = 1,475,

3x = 1,475 - 275 = 1,200,

x = 400.

So distance from Jimmy's house to school = 400 meters,

Distance from his school to the store = 400 + 100 = 500 meters,

Distance from the store to his house = 400 + 175 = 575 meters.

8 0

3 years ago