Let ƒ be a function that is differentiable on [a, b] .  we defined the average rate of change of ƒ over [a, b] to be ƒ(b) - ƒ(a)/( b - a) and the instantaneous rate of change of ƒ at x to be ƒ′(x). In this chapter we defined the average value of a function. For the new definition of average to be consistent with the old one, we should have ƒ(b) - ƒ(a)/( b - a) = average value of ƒ′ on [a, b]. Is this the case? Give reasons for your answer.

Q: Let f be defined as follows. y = f(x) = x² - 3x (a) Find the average rate of change of y with…

A: given function

Q: 500 Compute the average rate of change of the function, f(x) =x³+3x2 _ over the interval [5,10].

A: We have to find the average rate of change of the given function over the given interval.

Q: Consider the functionsƒ(x) = sin x and g(x) =4∏2 x(∏ - x).Compute and compare the average values of…

A: Average value of f(x)=sinx on [0,π] is given by: Average value of f(x) is 2/π.

Q: If f is a function and not necessarily a position function, then we can interpret AVa,a+h] as the…

A: This is a problem related to average and instantaneous rate of change of the function. Based on the…

Q: explain why the following statements are not completely true:    [f(a+h)-f(a)]/h is the secant line.…

A: To show that the two statements about the secant line are in general not true

Q: Use graphing technology to plot the given function together with its 3-unit moving average. f(x) =…

A: Solve the function

Q: 2. ㅠ to Suppose g(x) 4* = 1 (1+x²)²* the average value of f(x) on the interval [-1, 1] is equal 1 +…

A: We have to determine the function among the functions fx and gx having the smaller average value.…

Q: E. Set up the limit definition for finding the derivative of y = sin x.

A: Givne that  y=sinx  From the limit definition find the derivative of y=sinx

Q: Find

A: The average rate of change of f over the interval [1,b] is 2(b+1]  The detailed solution is as…

Q: How can a linear approximation be used to approximate the value of a functionf near a point at which…

A: Given that the linear approximation.

Exponential Growth Model

The relation that represents an exponential function is: