Question About Average Value of a Function on an Interval

Find the numbers b such that the average value of f(x)=2+6x-3x^2 on the interval [0,b] is equal to 3.

Solution Preview

This is actually an evaluation of the integral
∫f(x)= ∫2+6x-3x^2 dx in the [0, b] ...

Solution Summary

The bound of an interval that allows for a certain average value of a function is found. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

See the data in the attached file and answer the following questions.
Question 1
Construct a 95% confidence interval for an averagevalue of y given that x = 4. Remember the format is (x.xx, x.xx)
Question 2
Construct a 95% prediction interval for y given that x = 4.

Please help with the following problem. Provide step by step calculations for each.
The averagevalue of f(x) = 1/x on the interval [4, 16] is
(ln 2)/3
(ln 2)/6
(ln 2)/12
3/2
0
1
none of these
Find the area, in square units, of the region b

A ball is released at the top of a ramp (an inclined plane). The distance it travels can be expressed as the function:
s(t)=5t^2, where t is the time in seconds after the ball is released.
The distance function, s(t), is measured in feet. Find the average velocity of the ball for the time interval [1,4].

Let f(x), g(x) be functions defined on a closed bounded interval [a, b] such that the following conditions hold:
g is differentiable on [a, b].
There are positive constants a, b such that g(x) = a*f(x) - b*(dg/dx).
f(x) > 0 for all x in [a, b]
g(x) >= 0 for all x in [a, b]
g(a) > 0
-----------------------------

1. f(x)=X3-3X2+5 (-1,3)
I need to find local Maxima and Local Minima for this Question. Also determine where the function is increasing and where it is decreasing. round answer to two decimal places.
2. g(x)= X2+1
(a) Find the average rate of change from -1 to 2.
(b) Find an equation of the secant line containing

Please help with the following problem. Provide step by step calculations.
Prove that there is a bijection from the open interval (0, 1) to the half-open interval (0, 1].

An even function is defined as f(x) = f(-x), and an odd function has -f(x) = f(-x).
The domain of a function is the set of input data that keeps the function defined.
Determine if the function f(x) = -2x^2 * absolute value(-6x) is even, odd, or neither.
Find the average rate of change for the function f(x) = 4/(x+3) between t

36)If the functions f and g are defines for all real numbers and f is an antiderivative of g, which statements are not true?
I If g(x)>0 for all x, then f is increasing.
II If g(z)=0 then f(x) has a horizontal tangent at x+a.
III If f(x)=0 for all x, then g(x)=0 for all x.
IV If g(x)=0 for all x, then f(x)=0 for all x.

Which of the following is not needed to be known to calculate a confidence interval?
a. standard deviation
b. sample size
c. mean
d. degree of confidence