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Calculus graph please help

tresset_1 [31]

Answer:

See Below.

Step-by-step explanation:

We are given the graph of y = f'(x) and we want to determine the characteristics of f(x).

Part A)

f is increasing whenever f' is positive and decreasing whenever f' is negative.

Hence, f is increasing for the interval:

$(-\infty, -2) \cup (-1, 1)\cup (3, \infty)$

And f is decreasing for the interval:

$\displaystyle (-2, -1) \cup (1, 3)$

Part B)

f has a relative maximum at x = c if f' turns from positive to negative at c and a relative minimum if f' turns from negative to positive to negative at c.

f' turns from positive to negative at x = -2 and x = 1.

And f' turns from negative to positive at x = -1 and x = 3.

Hence, f has relative maximums at x = -2 and x = 1, and relative minimums at x = -1 and x = 3.

Part C)

f is concave up whenever f'' is positive and concave down whenever f'' is negative.

In other words, f is concave up whenever f' is increasing and concave down whenever f' is decreasing.

Hence, f is concave up for the interval (rounded to the nearest tenths):

$\displaystyle (-1.5 , 0) \cup (2.2, \infty)$

And concave down for the interval:

$\displaystyle (-\infty, -1.5) \cup (0, 2.2)$

Part D)

Points of inflections are where the concavity changes: that is, f'' changes from either positive to negative or negative to positive.

In other words, f has an inflection point wherever f' has an extremum point.

f' has extrema at (approximately) x = -1.5, 0, and 2.2.

Hence, f has inflection points at x = -1.5, 0, and 2.2.

7 0

2 years ago

3=x+3-5x what is the awnser

Nezavi [6.7K]

I know we aren’t suppose to promote other websites but photomath will scan these questions and give you an explanation quicker than live ppl answering them. Or tiger algebra or math papa all of these are great for solving algebra problems :)

8 0

2 years ago

Free to whoever gets it

liraira [26]

LolAnswer:

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Was is a macroeconomics

Cerrena [4.2K]

Answer:

Macroeconomics is a study that deals with the whole economy and everything pertaining to it.

Step-by-step explanation:

when we talk about Macroeconomics, we mean the whole economy. It can be related to a country's import or export, governance, how resources are accurately allocated to people in the country and the like.

4 0

3 years ago

Life Expectancies In a study of the life expectancy of people in a certain geographic region, the mean age at death was years an

Sphinxa [80]

Answer:

The probability that the mean life expectancy of the sample is less than X years is the p-value of $Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$ , in which $\mu$ is the mean life expectancy, $\sigma$ is the standard deviation and n is the size of the sample.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

We have:

Mean $\mu$ , standard deviation $\sigma$ .

Sample of size n:

This means that the z-score is now, by the Central Limit Theorem:

$Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

Find the probability that the mean life expectancy will be less than years.

The probability that the mean life expectancy of the sample is less than X years is the p-value of $Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$ , in which $\mu$ is the mean life expectancy, $\sigma$ is the standard deviation and n is the size of the sample.

8 0

2 years ago