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- Can the average rate of change of a function be constant?The accounting team at a manufacturing business developed a model for the company's profit over its first year of business. Their profit, in thousands of dollars, followed the graph of p(t)= (1/6)t3-t2+t where t is the number of months since January 1st. Use the mean value theorem to find the month in which the profits changed at the same rate as the average rate of change during the first 7 months. Midnight on New Year’s Eve corresponds to t=0,so for purposes of the mean value theorem, the first six months of the year correspond to the interval [0, 7]. Hint: Discard any solutions that are not in the corresponding open interval. Note: Use a calculator to determine the solution. Write your answer as the name of the month, not a number. For example, the value t=2.3 corresponds to some time in March, so you would say the answer is "March."approximate using linearization and use a calculator to compute the percentage error. e^−0.012
- Find the value of y between the points (2, y) and (5, − 1) with slope − 3.Monthly sales have been found to follow a linear trend of y = 10 + 8x, where y is the number of items sold and x is the number of the month. Monthly deviations from the trend have been calculated and follow an additive model. In month 12, the seasonal variation is estimated to be -6. What is the forecasted number of items to be sold in month 12?The accompanying data file shows the midterm and final scores for 32 students in a statistics course. a. Estimate a student’s final score as a function of his/her midterm score. b. Find the standard error of the estimate. c. Interpret the coefficient of determination.
- what is the average rate of change for f(z)=-2z2+4z-3over the interval (-1,4)Consider the function y = 4x3-3x2+6x-9. What is the average value of the function on [-2, 4] ?Visualize that two tributaries A and B at their confluence form a river C. Statistical properties of flow data for tributaries A and B indicate that tributary A has a yearly discharge rate smaller than its mean flow rate (?̅?) in 50% of the years while tributary B has a yearly discharge rate smaller than its mean flow rate (?̅?) in 60% of the time. In 70% of the years in which tributary A has a discharge rate smaller than its mean discharge rate (?̅?), tributary B also has a discharge rate smaller than its mean discharge rate (?̅?). Compute the probability that (i) both tributaries have a discharge rate smaller than their mean discharge rates, (ii) at least one tributary has a discharge rate smaller than its mean discharge rate, (iii) tributary A has a discharge rate smaller than its mean discharge rate given that tributary B has a discharge rate smaller than its mean discharge rate, (iv) at least one tributary has discharge rate higher than its mean discharge rate, and (v) probability…
- A person has invested some amount in the stock market. At the end of thefirst year the amount has grown by 25 percent profit. At theend of the second year his principal has grown by 40 percent and in the third year, there was a decline of 20%. What is the average rate of increase of his investment during the three years?What is the average rate of change Δy/Δx of: y = 1/x on the interval [1/2, 3/2]? 1/3 –2/3 –4/3 What is the average rate of change Δy/Δx of: y = 2x2 – 9 on the interval [4, b]? 2b + 8 2b2 – 23 2b2 – 32Find the point on the graph of y = (2x - 1)^3 + 6 where the normal line is vertical. Thanks
