The distance in feet that a ball rolls down an incline is modelled by the function s(t)=7t +4, where t in seconds after the ball begins rolling. Find the average- velocity of the ball over the time interval [4, 4.1].

Q: Consider the following function. f(x) = -x2 - 14x – 2 Find its average rate of change over the…

A: We have  fx=-x2-14x-2 Find the average rate of change of function fx over an interval a, b=-7, 1 is…

Q: If the position function of a moving object is S(t) =t - 3t + 2 meters from zero in t seconds, then…

A:

Q: Suppose that f(t) = 3t + 2 – 12t. а. What is the average rate of change of f (t) over the interval 2…

A: We are given the function f(t) = 3t+2-12t => f(t) = 2-9t. For (a), The average rate of change of…

Q: Suppose the fanetion f (t2=te Vepreseuts the Velocity cmeasured in meter/second) of an object at…

A: f(t)=te-2t

Q: At what time does f (t) attain its largest value?

A: Consider f(t) is any function. We know that function attains its largest or smallest value when the…

Q: Find the absolute extrema of the function on the closed interval.

A: Given function is  y=3-t-3,   -1, 5

Q: The velocity function (in meters per second) for a particle moving along a line is given by v(t) =…

A: Given, v(t)=t3-2t2   Interval [a,b]=[-2,3]

Q: For the function f (x) = a-5a2. (a) Evaluate the average rate of change from r = -2 to r 1 (b) What…

A: Given, The function fx=x3-5x2 We have to solve for part a and b

Q: If an object is dropped from the top of a building, its position in feet above the ground is given…

A: Concept of differentials need to be used here.

Q: Find the average rate of change of f(x)=--2x 2+4…

A:

Q: Find the maximu rate of change of the function f(x y) = x² + xy + y² at the point (6, 7). O 386 V653…

A: →Maximum rate of change of function is along gradient, which is given by,               ∇f(x,y) =…

Q: Find the average rate of change of f(x)=5x^2-3 on the interval [2,t]. Answer with an expression…

A:

Q: Given f(x) = V2x – 3, find the average rate of change on the interval2, . %3D

A:

Q: Find the linearization of the function F(X) =sqrt (x+3) at a= 1 and use it to approximate the…

A: Therefore linearization at a = 1 is,

Q: Two cars start at the same time and travel in the same direction along a straight road.  The…

A: Given velocity of car A and car B as a function of time t is,

Q: a particle moves according to the function s(t)= t^2 - 2t +5,  what is the instantaneous velocity of…

A: A particle moves according to the function s(t)=t2-2t+5

Q: If a ball is thrown in the air with a velocity 48 ft/s, its height in feet t seconds later is given…

A:

Q: If a ball is thrown in the air with a velocity 42 ft/s, its height in feet t seconds later is given…

A:

Q: Let v(t) = t2 -2t-5 be the velocity function for a particle moving along a straight line. Here,…

A:

Q: Suppose the position function of a moving object is given by s (æ) = Væ. Then the average velocity…

A: Given that: To find:

Q: For time t > 0, a particle moves along the x-axis, its position is given by the function s(t) = -t*…

A:

Q: A Ferrari's position at time t is given by s(t) = t3 - 9t2 + 24t 2) What is the Ferrari's velocity…

A: Given:    s(t) = t3 - 9t2 + 24 t   Velocity at t = 0

Q: Find the average rate of change of the function f(x) = - 2x – 7x + 8, over the interval [-1,1]. -…

A:

Q: at time t20, the velocity of a body moving along the s-axis is v=t - 7t+ 6. When is the body's…

A: Explanation and solutions is given below....

Q: Consider the function f(x) = -3x²³ +3x²-3x -\ Find average rate of change on interval (-4,-1). Find…

A:

Q: The height in meters of a diver above the pooľ's surface is given by h(t) = -5t² + 7t + 10, where t…

A: Given that the height of a diver above the pool's surface is  ht=-5t2+7t+10 a) It is required to…

Q: Find the approximate value of second derivative f"(0) with the step h for the following function by…

A:

Q: (b) If a rock is thrown upwared on the planet mars with a velocity of 12ms, its height in meters t…

A: The height of the rock is given by: y(t)=12t-1.92t2 To find the average velocity over the interval…

Q: Suppose that f(t)3t +2t-3. What is the average rate of change of f(t) over the interval 1 to 2? %3D…

A: Consider the function  f(t)=t2+2t−3

Q: nen does the particle reach a velocity of 137 m/s if its position function is given by:…

A:

Q: The height of an arch above the ground is given by the function y=10sinx, for 0 <= x<= pi .…

A: The given interval is [0,π] So, a=0, b= π

Q: for f(x)=3x^2, find the average rate of change of the function over the interval [0,2].

A: For the function fx=3x2, to find the average rate of change of the function over the interval [0,2].…

Q: The distance of a body travels as a function of time and is defined by x(t) = 18t + 9t^2. What is…

A: Given that: Distance travelled by the body is given by:             x(t)=18t+9t2

Q: Find the average rate of change of f(x)=3x^2−9 on the interval [1,t].  (answer with an expression…

A: We have to find average rate of change of f(x) on the interval [1,t]

Q: Find the average rate of change for the function between the given values. 18) f(x) = 4x2; from 0 to

A: The average rate of change of a function f(x) on the interval [a, b] is fb-fab-a. The given function…

Q: The position of a moving object is given by the function s (t) = 4t² – 10. What is the instantaneous…

A:

Q: If a rock is thrown upward on the planet Mars with a velocity of 12 m/sec, its height (in meters) t…

A:

Q: Use the sign pattern for the derivative dƒ/ dx = 6(x - 1)(x - 2)^2(x - 3)^3(x - 4)^4 to identify the…

A:

Q: The average speed f(t) (measured in kph) of traffic in a certain municipality between 4 PM to 8 PM…

A: It is given that the average speed of traffic is approximated by the function ft=20t-40t+50. We have…

Q: T* dx from a=-1 to b-1 is an even function.

A:

Q: The distance in feet that a ball rolls down an incline is modelled by the function s(t)=8r +2,where…

A: topic - average value of function

Q: Find the average rate of change of f(x) = 6x? - 2 on the interval (3, a].

A:

Q: If a ball is thrown vertically upward from the roof of 4848 foot building with a velocity of 6464…

A: s(t) = 48 + 64t - 16t2Hence, s’(t) = 64 – 32ts”(t) = - 32When s is maximum, s’(t) = 0; hence 64 –…

Q: Find f'(a) using the definition of the derivative at a point for f(x) = 1 VI at a = 7.

A:

Q: Given the function g(x) = the function over the interval-11SA-1. + 10x + 18, determine the average…

A:

Q: Find the average velocity of an object for the interval 1<t< 3, if its position is given by s = = t²…

A: Differentiate the function to find the velocity function. dsdt=2t+5

Q: Find the average rate of change of f(x) = 6x² – 7 over the interval [-3,1]. %3D

A: Given data: *The function f(x) is, f(x)=6x2-7 *The interval defined for the function is [-3,1]. The…

Q: A particle is moving in a straight line according to the linear position function s(t)=t^3−9t^2+…

A: To find: The total distance traveled by the particle in first 6 second. Given: The position function…

Q: Given: f (x) = 15(-)*, calculate the average rate of change of f over the interval -1sxsl. %3D Show…

A: Given that       f(x) = 15(1/3)x Here we have to find the average rate of change of f over the…

Q: At time t seconds, the center of a bobbing cork is 2sin(2t) centimeters above or below water level.…

A: ft=2sin2t Now velocity is the derivative of position with respect to time. So differentiating…

Exponential Growth Model

The relation that represents an exponential function is: