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4 years ago

Investigate the existence of a extrema value, what does the markered part mean?

Mathematics

1 answer:

OLga [1]4 years ago

5 0

Answer: We have

f'(x) = a x + b,

f'(x) = 0 at x = -b/a

f(x) = a x^2 / 2 + b x + c

Meaning of marked part

❟ ∵ a<0 ❟ f is a quadratic function

∴ f has absolute maximum value at x = -b/a

For all a with a less than zero, f is a quadratic function. Therefore f has a global maximum at x = -b/a

That typesetting seems very sloppy. It probably is supposed to be

∀a < 0, f is a quadratic function.

The second sentence is sloppy in use of "absolute". It can't mean absolute value, so presumably it means "global".

Sometimes a minimum or maximum is only local, but a quadratic function has exactly one extrema, and it is global. And if a < 0, the extrema is a global maximum.

Step-by-step explanation:

An extrema (minimum or maximum) for f(x) occurs only where f'(x) = 0, that is, when the slope of the tangent at x is zero.

But if the function crosses its tangent at that point, the point is an inflection point, not an extrema. A quadratic never crosses it's tangent.

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Select the correct answer.

Pani-rosa [81]

Answer:

its probably division property if equality

Step-by-step explanation:

because it has division in it

6 0

3 years ago

Factorize: x²+2+1/x²

andrew-mc [135]

$x^{2}+\frac{1}{x^{2}}+2=\boxed{\left(x+\frac{1}{x} \right)^{2}}$

8 0

2 years ago

The effect of a monetary incentive on performance on a cognitive task was investigated. The researcher predicted that greater mo

riadik2000 [5.3K]

Answer:

1) $H_0:\mu_5=\mu_{25}=\mu_{50}$

2) $H_a:\mu_{50}>\mu_{25}>\mu_{5}$

3) A Type I error happens when we reject a null hypothesis that is true. In this case, that would mean that the conclusion is that there is evidence to support the claim that the greater the incentive, the more puzzles are solved, but that in reality there is no significant difference.

4) A Type II error happens when a false null hypothesis is failed to be rejected. In this case, that would mean that there is no enough evidence to support the claim that the greater the incentive, the more puzzles are solved, but in fact this is true.

5) The probability of a Type I error is equal to the significance level, as this is the chance of having a sample result that will make the null hypothesis be rejected.

Step-by-step explanation:

As the claim is that the greater the incentive, the more puzzles were solved, the null hypothesis will state that this claim is not true. That is that there is no significant relation between the incentive and the amount of puzzles that are solved. In other words, the mean amount of puzzles solved for the different incentives is equal (or not significantly different):

$H_0:\mu_5=\mu_{25}=\mu_{50}$

The research (or alternative hypothesis) is that the greater the incentive, the more puzzles were solved. That means that the mean puzzles solved for an incentive of 50 cents is significantly higher than the mean mean puzzles solved for an incentive of 25 cents and this is significantly higher than the mean puzzles solved for an incentive of 5 cents.

$H_a:\mu_{50}>\mu_{25}>\mu_{5}$

A Type I error happens when we reject a null hypothesis that is true. In this case, that would mean that the conclusion is that there is evidence to support the claim that the greater the incentive, the more puzzles are solved, but that in reality there is no significant difference.

A Type II error happens when a false null hypothesis is failed to be rejected. In this case, that would mean that there is no enough evidence to support the claim that the greater the incentive, the more puzzles are solved, but in fact this is true.

The probability of a Type I error is equal to the significance level, as this is the chance of having a sample result that will make the null hypothesis be rejected.

4 0

3 years ago

Two step Equation a.3x-8=31

stira [4]

Simplifying 3x + -8 = 31 Reorder the terms: -8 + 3x = 31 Solving -8 + 3x = 31 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + 3x = 31 + 8 Combine like terms: -8 + 8 = 0 0 + 3x = 31 + 8 3x = 31 + 8 Combine like terms: 31 + 8 = 39 3x = 39 Divide each side by '3'. x = 13 Simplifying x = 13

5 0

3 years ago

Read 2 more answers

With a height of 68 in, Nelson was the shortest president of a particular club in the past century. The club presidents of the

Ivahew [28]

Answer:

a. The positive difference between Nelson's height and the population mean is: $\\ \lvert 68-70.7 \rvert = \lvert 70.7-68 \rvert\;in = 2.7\;in$ .

b. The difference found in part (a) is 1.174 standard deviations from the mean (without taking into account if the height is above or below the mean).

c. Nelson's z-score: $\\ z = -1.1739 \approx -1.174$ (Nelson's height is below the population's mean 1.174 standard deviations units).

d. Nelson's height is usual since $\\ -2 < -1.174 < 2$ .

Step-by-step explanation:

The key concept to answer this question is the z-score. A z-score "tells us" the distance from the population's mean of a raw score in standard deviation units. A positive value for a z-score indicates that the raw score is above the population mean, whereas a negative value tells us that the raw score is below the population mean. The formula to obtain this z-score is as follows:

$\\ z = \frac{x - \mu}{\sigma}$ [1]

Where

$\\ z$ is the z-score.

$\\ \mu$ is the population mean.

$\\ \sigma$ is the population standard deviation.

From the question, we have that:

Nelson's height is 68 in. In this case, the raw score is 68 in $\\ x = 68$ in.
$\\ \mu = 70.7$ in.
$\\ \sigma = 2.3$ in.

With all this information, we are ready to answer the next questions:

a. What is the positive difference between Nelson's height and the mean?

The positive difference between Nelson's height and the population mean is (taking the absolute value for this difference):

$\\ \lvert 68-70.7 \rvert = \lvert 70.7-68 \rvert\;in = 2.7\;in$ .

That is, the positive difference is 2.7 in.

b. How many standard deviations is that [the difference found in part (a)]?

To find how many standard deviations is that, we need to divide that difference by the population standard deviation. That is:

$\\ \frac{2.7\;in}{2.3\;in} \approx 1.1739 \approx 1.174$

In words, the difference found in part (a) is 1.174 standard deviations from the mean. Notice that we are not taking into account here if the raw score, x, is below or above the mean.

c. Convert Nelson's height to a z score.

Using formula [1], we have

$\\ z = \frac{x - \mu}{\sigma}$

$\\ z = \frac{68\;in - 70.7\;in}{2.3\;in}$

$\\ z = \frac{-2.7\;in}{2.3\;in}$

$\\ z = -1.1739 \approx -1.174$

This z-score "tells us" that Nelson's height is 1.174 standard deviations below the population mean (notice the negative symbol in the above result), i.e., Nelson's height is below the mean for heights in the club presidents of the past century 1.174 standard deviations units.

d. If we consider "usual" heights to be those that convert to z scores between minus2 and 2, is Nelson's height usual or unusual?

Carefully looking at Nelson's height, we notice that it is between those z-scores, because:

$\\ -2 < z_{Nelson} < 2$

$\\ -2 < -1.174 < 2$

Then, Nelson's height is usual according to that statement.

7 0

3 years ago