
Consider the following function. f(t) = 3t2 − 3 (a) Find the average rate of change of the function below over the interval [3, 3.1]. (b) Compare this average rate of change with the instantaneous rates of change at the endpoints of the interval. (at t = 3) (at t = 3.1)

Could someone help me with these questions, I don't know question c) and d) Consider the function f(x) = (0.1x1)(x+2)^2. a) Determine the function's average rate of change on 2<x<6. Answer; Avg rate of change is 3.2 b) Estimate the instantaneous rate of change at x=2...

Could someone help me with these questions, I don't know question c) and d) Consider the function f(x) = (0.1x1)(x+2)^2. a) Determine the function's average rate of change on 2<x<6. Answer; Avg rate of change is 3.2 b) Estimate the instantaneous rate of change at x=2...

Given the function: f(x)=x^34x^2+6x3 a) Find the average rate of change of the function on the interval [2,4] b)find the instantaneous rate of change of the function at x=3.

consider the function f(x)=x^26x+12 a. find the average rate of change over the interval [1,3] b. use the definition of the derivative to find f prime(x) c. find the instantaneous rate of change at the point where x=3 d. find the value of x on the interval [1,3] such that f...


Find the average rate of change f(x)=x^38x+9 a. from 3 to 2 b. from 1 to 5 c. from 5 to 9 A. what is average rate of change of f(x)=x^38x+9 from 3 to 2? B. what is the average rate of change of f(x)x^38x+9 from 1 to 5? C. what is the average rate of change of f(x)=x^...

Verify if question a is correct I calcuated twice now and I am getting 0 as an answer. I don't understand question b a) Examine the function f9x) =2(0.5x1)^2(x+2)^2. Determine the function's average of change from 2<x<2. I got answer: =00/22 =0 Avg rate of change: 0...

Given the function f(x) = 2(3)^x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3. Part A: Find the average rate of change of each section. Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of ...

i'm not sure how to do this. can someone help, please? thanks! consider the function f(x0 = x^2 + 2x on the interval [2, 2] a. draw a sketch of the graph of f(x). find the average rate of change on the interval [2, 2] and sketch this secant line. b. find an expression that ...

Two functions, A and B, are described as follows: Function A y = 9x + 4 Function B The rate of change is 3 and the yintercept is 4. How much more is the rate of change of function A than the rate of change of function B? 2 3 6 9 I believe the answer is either C or B but I am ...

Find the average rate of change in height of the orange from t=2 to t=5 (in feet per second) The equation is h (t)=605+15t4.9t^2 in feet. I know the the average rate of change is change in q/ change in time. Do I put t=3 and subtract the quantity of 5 and 2 in the formula for...

To find the domain of a function from its graph... To find the range of a function from its graph... To approximate the relative minimum or maximum of a function using a graphing utility,... Let a(,f(a)) and (b,f(b)) be two points on the graph of a nonlinear function f. The ...

You are working as assistant to a major movie producer from Hollywood, but mainly you look after prerelease film publicity. You are an old hand at publicity, having worked in several production companies before. Based on previous experience you have developed a model for the ...

Create a graph of a function given the following information: The instantaneous rate of change at x = 2 is zero. The instantaneous rate of change at x = 3 is negative. The average rate of change on the interval 0 <x <4 is zero.

For the function f(x) = 5/x+4 find the average rate of change of f from 1 to x:


for f(x)=x^2 +1, which value is the largest magnitude? a) average rate of change from x=1 to x=1 b) instanteneuous rate of change at x=3 c) instanteneous rate of change at x=0 average rate of change from x=4 to x=0

Please help.. Determine the value of "g" so that the average rate of change of the function h(x)=x^2+3x+2 on the interval 3≤x≤g is 1. Thank you.

Please help.. Determine the value of "g" so that the average rate of change of the function h(x)=x^2+3x+2 on the interval 3≤x≤g is 1. Thank you.

Please help.. Determine the value of "g" so that the average rate of change of the function h(x)=x^2+3x+2 on the interval 3≤x≤g is 1. Thank you.

How do i find the average rate of change of the function f(x)=5x from x1=0 to x2=3 .....im so confused

for the function f(x)=7/x+6, find the average rate of change of f from 1 to x.

For the function, find the average rate of change of f from 1 to x:f(x)f(1)/x1 x does not equal 1 f(x) = x3 + x

Find the average rate of change of g(x) = 2x2 + 36x  142 on the interval from x = 5 to x = 10.

find the average rate of change for the function f(x)=60x3x^2 between x=6 and x=19

Find the average rate of change on the interval [6,3] of the function h(x)=x^24x+7. A. 7 B. 7 C. 1 D. 13 E. 5


Find the average rate of change for function f(x)=3x^(2)5 at the points x[1]=6 and x[2]=10

find the average rate of change between f(4) and f(1) in the function f(x)= x^2+2x8

find the average rate of change of the function f(x)=x^3+1 over the interval [1,1]

Find the average rate of change for the function between the give values. f(x)=4x + 8; from 1 to 2

For the function f(x)= 8/x+7,find the average rate of change of f from 1 to x.

for the function f(x)=5/x+4, find the average rate of change of f from 1 to x. please show work

Joe is investigating the rate of change of the function y=cos x on the interval xE[0,2π]. He notices that the graph of y=cos x passes through the xaxis at 45°. He also determines the instantaneous rate of change at x = 0, π, and 2π by inspection. Based on this...

Joe is investigating the rate of change of the function y=cos x on the interval xE[0,2π]. He notices that the graph of y=cos x passes through the xaxis at 45°. He also determines the instantaneous rate of change at x = 0, π, and 2π by inspection. Based on this...

g(t)=2+cos t; [0,pi] Can you help me find the average rate of change of the function over the given interval?

If f is a function such that [(f(b)f(a))/(ba)]=2 , then which of the following statements must be true? a.f(a) = f(b) = 2 b.The slope of the tangent line to the function at x = a is 2. c.The average rate of change of the function on the interval [a, b] is 2 d.The linear ...


Given the numerical values shown for the function f(x), find approximate values for the derivative of f(x) at each of the xvalues given. x= 0 1 2 3 4 5 6 7 8 f(x)= 13 15 16 17 17 14 11 9 7 f'(x)= 2 1 1 1 0 3 3 2 2 What seems to be the greatest rate of change of f(x)? rate...

Let h(12) = 100 for some function h(x), defined everywhere. If the average rate of change of h(x) from x = 12 to x = 20 is 50, then find h(20).

Let f be the function defined by f(x)= sqrt(x), 0 <or= x <or= 4. and f(x)= 6x, 4 < x <or= 6 a. Is f continuous at x=4? justify. b. Find the average rate of change of f(x) on the closed interval [0,6]. c. suppose the function g(x)= k sqrt(x), 0 <or= x <or= 4...

h(t)=cos t, [pi/4, 3pi/4] find the average rate of change of the function over the given interval or intervals

The table below represents the velocity of a car as a function of time: Time (hour) x Velocity (miles/hours) y 0 50 1 52 2 54 3 56 Part A: What is the yintercept of the function, and what does this tell you about the car? Part B: Calculate the average rate of change of the ...

A function is given below. Determine the average rate of change of the function between t = 9 and t = 9 + h. f(t) = Square root of 4t

Find the average rate of change from x = 10 to x =17 for the function f(x) = 0.01(2) ^x and select the correct answer below A. 10.24 B. 185.78 C. 1300.48 D. 1310.72 Is it A?

Let f be defined as follows. F(x)=y=x^2 7 (a) Find the average rate of change of y with respect to x in the following intervals. from x = 4 to x = 5 from x = 4 to x = 4.5 from x = 4 to x = 4.1 (b) Find the (instantaneous) rate of change of y at x = 4

Let f be defined as follows. y=f(x)=x^212x (a) Find the average rate of change of y with respect to x in the following intervals. from x = 5 to x = 6 ?? from x = 5 to x = 5.5 ?? from x = 5 to x = 5.1 ?? (b) Find the (instantaneous) rate of change of y at x = 5. ??

is average rate of change and average value the same or will you get a different answer for each this is calculus so it's the mean average. it's using the formula and integrating. I don't understand your question, but I can assure you that average rate of change and average ...


Let f be defined as follows. y = f(x) = x^2  4 x (a) Find the average rate of change of y with respect to x in the following intervals. from x = 5 to x = 6 from x = 5 to x = 5.5 from x = 5 to x = 5.1 (b) Find the (instantaneous) rate of change of y at x = 5. 4

Let f be defined as follows. F(x)=y=x^2 7 (a) Find the average rate of change of y with respect to x in the following intervals. from x = 4 to x = 5 from x = 4 to x = 4.5 from x = 4 to x = 4.1 (b) Find the (instantaneous) rate of change of y at x = 4.

Find the average rate of change from x = 10 to x =17 for the function f(x) = 0.01(2) ^x and select the correct answer below A. 10.24 B. 185.78 C. 1300.48 D. 1310.72 Is it C?

Joe is investigating the rate of change of the function y=cos x on the interval xE[0,2π]. He notices that the graph of y=cos x passes through the xaxis at 45°. He also determines the instantaneous rate of change at x = 0, π, and 2π by inspection. Based on this...

The table below represents the velocity of a car as a function of time: Time (hour) x Velocity (miles/hours) y 0 50 1 52 2 54 3 56 Part A: What is the yintercept of the function, and what does this tell you about the car? (4 points) Part B: Calculate the average rate of ...

The table below represents the distance of an airplane from its destination as a function of time: Time (hours) x Distance (miles) y 0 2,700 1 2,160 2 1,620 3 1,080 4 540 Part A: What is the yintercept of the function, and what does this tell you about the airplane? (4 points...

Joe is investigating the rate of change of the function y=cos x on the interval xE[0,2π]. He notices that the graph of y=cos x passes through the xaxis at 45°. He also determines the instantaneous rate of change at x = 0, π, and 2π by inspection. Based on this...

The graph represents function 1 and the equation represents function 2: A graph with numbers 0 to 4 on the xaxis and yaxis at increments of 1. A horizontal straight line is drawn joining the ordered pairs 0, 3 and 4, 3. Function 2 y = 3x + 1 How much more is the rate of ...

The graph represents function 1 and the equation represents function 2: A graph with numbers 0 to 4 on the xaxis and yaxis at increments of 1. A horizontal straight line is drawn joining the ordered pairs 0, 3 and 4, 3. Function 2 y = 2x + 1 How much more is the rate of ...

The graph represents function 1 and the equation represents function 2: A graph with numbers 0 to 4 on the xaxis and yaxis at increments of 1. A horizontal straight line is drawn joining the ordered pairs 0, 3 and 4, 3. Function 2 y = 4x + 1 How much more is the rate of ...


Samuel is investigating the rate of change of the function f(x) = cos x on the interval xE[0, 2pi]. He notices that the graph of f(x) passes through the xaxis at pi/2. He also determines the instantaneous rate of change at x = 0, pi and 2pi by inspection. Based on this ...

y = f(x) = x^2  6 x (a) Find the average rate of change of y with respect to x in the following intervals. from x = 2 to x = 3 from x = 2 to x = 2.5 from x = 2 to x = 2.1 (b) Find the (instantaneous) rate of change of y at x = 2.

Let F(s)=5s2+1s+4. Find a value of d greater than 0 such that the average rate of change of F(s)from 0 to d equals the instantaneous rate of change of F(s)at s=1.

Let F(s)=5s2+5s+4 . Find a value of d greater than 0 such that the average rate of change of F(s) from 0 to d equals the instantaneous rate of change of F(s) at s=1. d=

The wind chill is the temperature, in degrees Fahrenheit, a human feels based on the air temperature, in degrees Fahrenheit, and the wind velocity (v), in miles per hour (mph). If the air temperature is 32degrees Fahrenheit, then the wind chill is given by W(v)=55.622.1v^.16 ...

The wind chill is the temperature, in degrees Fahrenheit, a human feels based on the air temperature, in degrees Fahrenheit, and the wind velocity (v), in miles per hour (mph). If the air temperature is 32degrees Fahrenheit, then the wind chill is given by W(v)=55.622.1v^.16 ...

What is the instantaneous slope of y =8/x at x = 3? What is the average rate of change of y with respect to x over the interval [3, 4] for the function y = 2x + 2? The surface area, S, of a sphere of radius r feet is S = S(r) = 4πr2. Find the instantaneous rate of ...

f(x)=3.1ã(x+19 1.Decribe the graph be obtained using transformations of the square root function. First, vertically stretch the graph of f (x) = by the factor 3.1; then shift the results up 19 units. 2.Determine how to tell the model describes the actual height of a four ...

find the average rate of change f(x)=x^2 + 2x between x=0 and x=6 can anyone please help me explain why the answer is 8? thank you!

Find the average rate of change h(x)=2x^24 from x=2 to x=6 Simplify your answer as much as possible


Hey so I need help on a problem from an assignment that my teacher won't help at all. WRITE IN COMPLETE SENTENCES "An oil strikes a sand bar that rips a hole in the hull of the ship. Oil begins leaking out of a tanker with spilled oil forming an approximate circle around the...

find the average rate of change from 1 to x Find the average rate of change from 1 to 3 Using f(x) = 2x^2+6x

find the average rate of change from 1 to x Find the average rate of change from 1 to 3 Using f(x) = 2x^2+6x

Find the average rate of change of the function f(x) = 2x4 + 3x2 ¡ x + 2: (a) on the interval [0; 3] and (b) on the interval [¡2; 0]

The function gives the cost to manufacture x items. C(x) = 20,000 + 5x − x2 20,000 ; x = 20,000 Find the average cost per unit of manufacturing h more items (i.e., the average rate of change of the total cost) at a production level of x, where x is as indicated and h = ...

If we know that for a function, f(x), that f(2) = 6 and f(5) = 1, what is the average rate of change of f(x) on the interval [2,5]?

what is the average rate of change for the function g(x)=3x^24 over the interval (1,3)?

Find the average rate of change of f(x)=6x²−3 on the interval [2,a]. Your answer will be an expression involving a What I did so far: I found f(2) which is 21 and that would make the function (2,21) Then, I found f(a) which is 6a^23 and that would make the function (a,6a^23)

Bob is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after n days: F(N)=10(1.02)^n 1. Starting from 0 days, plug xvalues into our function to find out how many days it takes for the plant to...

The average daily metabolic rate for rodents can be expressed by the function m=85.65w^0.54, where w is the weight in kg and m is the metabolic rate in kcal/day. Determine the rate of change in the metabolic rate with respect to time for a 0.25kg rodent that is gaining weight ...


Please help.. Joe is investigating the rate of change of the function y=cos x on the interval xE[0,2π]. He notices that the graph of y=cos x passes through the xaxis at 45°. He also determines the instantaneous rate of change at x = 0, π, and 2π by inspection...

A function is given. Determine the average rate of change of the function between the given values of the variable. f(t) = 6/t ; t = a, t = a + h

A function is given. Determine the average rate of change of the function between the given values of the variable. f(x) = 6 âˆ’ x2; x = 1, x = 1 + h

A function is given. Determine the average rate of change of the function between the given values of the variable. f(x) = 6 − x2; x = 2, x = 2 + h

If the average rate of change of g(x) from x = 1 to x = 9 is 20, and if the average rate of change of g(x) from x = 9 to x = 21 is 40, then what is the average rate of change of g(x) from x = 1 to x = 21?

1. Find the average rate of change of f(x)=x^39x+9: a) from 8 to 2 b) from 1 to 1 c) from 1 to 4 a) what is averge rate of change of f (x) =x^39x+9 from 8 to 2?

Determine the value of 'a' so that the average rate of change of the function h(x)=x^2+3x+2 on the interval 3<=x<=a is 1

What is the average rate of change of the function f, given by f(x) = x2 + 1, on the interval [2,5]?

h(t)=cot t a.) [pi/4,3pi/4] b.) [pi/6,pi/2] Find the average rate of change of the function over the give n interval and intervals. Please show step by step instructions. Thanks

1. Let f be a twicedifferentiable function such that f (2) = 8 and f (4) = 5. Which of the following must be true for the function f on the interval 2 ≤ x ≤ 4. I. The average value of f is 6.5 II. The average rate of change of f is 1.5 III. The average value of f...


Determine the average rate of change form x = 1 to x = 4 for each function. a) y= x b) y=x^2 c) y=x^3 d) y=7

What is the average rate of change of the function f(x)=20(1/4)^x from x = 1 to x = 2? Enter your answer as a decimal. Do not round.

The position function of an object moving along a straight line is given by s = f(t). The average velocity of the object over the time interval [a, b] is the average rate of change of f over [a, b]; its (instantaneous) velocity at t = a is the rate of change of f at a. A ball ...

Find the average rate of change of the function over the given interval. You must reduce and simplify your answer, if possible. a. f(x)=cot x, [pi/6, pi/2] b. f(theta)= 2 + cos (theta), [pi, 0]

Determine which function has the greater rate of change 1.The rates of change are equal. 2.The graph has a greater rate of change. 3.The table has a greater rate of change. 4.none of the above file:///C:/Users/SCHOOL/Pictures/math.JPG HELP ME UNDERSTAND THIS PLEASE??

file:///C:/Users/SCHOOL/Pictures/math.JPG Determine which function has the greater rate of change 1.The rates of change are equal. 2.The graph has a greater rate of change. 3.The table has a greater rate of change.*** 4.none of the above Is this right?

If the average rate of change of g(x) from x = 1 to x = 5 is 17.5, and if the average rate of change of g(x) from x = 5 to x = 10 is 35, then what is the average rate of change of g(x) from x = 1 to x = 10?

which two points of a trignometric function will always give an average rate of change of 0?

which two points of a trignometric function will always give an average rate of change of 0?

Please Help ; what does the average rate of change tell you about the function on the interval ?


I have three questions I need help solving 1) A ball's position, in meters, as it travels every second is represented by the position function s(t) = 4.9t2 + 550. What is the velocity of the ball after 3 seconds? 2) The cost in dollars of producing x units of a particular ...

The question that I'm stuck on is this: "Let f(x,y)= x^(2)*ln(y). Find the average rage of change of f as you go from (3,1) to (1,2) and find the instantaneous rate of change of f as you leave the point (3,1) toward (2,1)." Any help would be appreciated. Thanks!

The number of gallons of water remaining in a swimming pool t minutes after the drains are opened and the pool begins emptying is give given by the function f(x)=40t^23000t+40,000 gallons. Between 3 and 5 minutes after the drains were opened, the pool emptied at an average ...

g(x)=4/x; x=5, x=5+h Determine the average rate of change of the function between the given values of the variable.

a) Describe a graph for which the average rate of change is equal to instantaneous rate of change for its entire domain. Describe a real life situation that this graph could represent. b) Describe a graph which the average rate of change between two points is equal to the ...
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