Answer:
the first diagram
Step-by-step explanation:
first one
First, you need to find the derivative of this function. This is done by multiplying the exponent of the variable by the coefficient, and then reducing the exponent by 1.
f'(x)=3x^2-3
Now, set this function equal to 0 to find x-values of the relative max and min.
0=3x^2-3
0=3(x^2-1)
0=3(x+1)(x-1)
x=-1, 1
To determine which is the max and which is the min, plug in values to f'(x) that are greater than and less than each. We will use -2, 0, 2.
f'(-2)=3(-2)^2-3=3(4)-3=12-3=9
f'(0)=3(0)^2-3=3(0)-3=0-3=-3
f'(2)=3(2)^2=3(4)-3=12-3=9
We examine the sign changes to determine whether it is a max or a min. If the sign goes from + to -, then it is a maximum. If it goes from - to +, it is a minimum. Therefore, x=-1 is a relative maximum and x=1 is a relative miminum.
To determine the values of the relative max and min, plug in the x-values to f(x).
f(-1)=(-1)^3-3(-1)+1=-1+3+1=3
f(1)=(1)^3-3(1)+1=1-3+1=-1
Hope this helps!!
Draw from (3, -1.5) to (-2, 6)
Answer:
A) D
B) B
C) C
D) B
Step-by-step explanation:
The complete question is:
A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for random sampleof 1044 people age 15 or older, the mean amount of time spent eating or drinking per day is 1.44 hours with a standarddeviation of 0.57 hour. (A.) A histogram of time spent eating and drinking each day is skewed right. Use the result to explain why a large samplesize is needed to construct a confidence interval for the mean time spent eating and drinking each day.A. The distribution of the sample mean will never be approx. normalB. The distribution of the sample mean will always be approx. normalC. Since the distribution of time eating and drinking each is normally distributedthe sample must be large so that the distribution of the sample mean will be apprx. NormalD. Since the distribution of time spent eating and drinking each day is not normally distributed (skewed right), the sample must be large so that the distribution of the sample mean will be approx. normal.
(B) In 2010, there were over 200 million people nationally age 15 or older. Explain why this, along with the fact that that the data were obtained using a random sample, satisifies the requirements for constructing a confidence interval.A. The sampe size is greater than 5% of the population.B. The sample size is less than 10% of the populationC. The sample size is greater than 10% of the populationD. The sample size is less than 5% of the population.
(C.) Determine and interpret a 95% confidence interval for themean amount of time Americans age 15 older spend eating and drink each day.A. the nutritionist is 95% confident that the mean amount of time spent eatingand drinking per day is between blank and blank hours.B. the nutritionist is 95% confident that the amount of time spent eating or drinking per day forany individuals is between blank and blank hours.C. There is a 95% probability that the meant amount of time spent eating or drinking per day is between blank and blank hours.D. The requirements for constructing a confidence interval are not satisfied.
(D) Could the interval be used to estimate the mean amount of time a 9 year old spends eating and drinking each day?A. No, the interval is about individual time spent eating or drinking per day and cannot be used to find the mean time spent eating or drinking per day.B. No the intreval is about people age 15 or older. The mean amount of time spent eatinf or drinking per day for 9 year olds may differ.C. Yes, the interval is about individual time spent eating or drinking per dat and can be used to find the mean amount of time a 9 year old spends eating and drinking each day.D. Yes, the interval is about the mean amount of time spent eating or drinking per day for the 9 year olds.E. A confidence interval could not be constructed in part (C)D
A) a large sample size ensures normal distribution
B) a good sample size is around 10% of the population
C) confidence interval is a range of value and defines probability that mean of the population will lie with in the range
D) The data given is for 15 years and older so it can't be used for 9 years and younger
