An object moves according to the function h(t) = -t² + 13, where h(t) is the height, in meters, and t is the time, in seconds. What is the average rate of change of the height of the object during the first 3 seconds the object is in motion?

Q: Find the average rate of change of the function f(x) = 2x² + 16x + 28 on the interval [-3, –3 + h].

A:

Q: Given the function h(x) = –x² – 6x + 17, determine the average rate of change of the function over…

A:

Q: Find the average rate of change of f(x)=3x2 +2x−2 on the interval [2,t].

A: Consider the function f ( x ) on the interval [ 2,t ],

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: 4) How quickly is an airplane's elevation currently rising if its height (in feet) as a function of…

A: We need to find rate of change of elevation or rate of change of height when t = 4 sec Hence we will…

Q: Between 2006 and​ 2016, the number of applications for​ patents, N, grew by about 4.3​% per year.…

A: To solve the following problem

Q: Q5 Find the instantaneous rate of change at 2 for: f(x) = 6x2-9x -6

A: The given function is,

Q: find the average rate of change from f(4) to f(10) in the function f(x)=x2+3

A: We have to find the average rate of change from f(4) to f(10) in the function f(x) = x2 + 3 We know…

Q: Let f(x) = -x² - 4x + 11. What is the average rate of change from x = -5 to x = 2? %3! O-7

A:

Q: Use differentials to approximate the change in R revenue= 50x-1.5x2 as sales increase from 13 to 15…

A: Consider the given function: R=50x-1.5x2 Now differentiate the given function: dRdx=50-3xdR=50-3xdx

Q: The function f(x) = x2 describes the area of a square, f(x), in square inches, whose sides each…

A: Given function fx=x2 To find rate of change of area.

Q: An accessories company finds that the cost, in dollars, of producing x belts is given by C(x) = 780…

A: Given :  Cost function :  C ( x ) = 780 + 35 x - 0.063x2  Find the rate at which average cost is…

Q: Find the average rate of change of f(x) = 3x-1 on the interval [2, 10].

A:

Q: The function f(x) = x2 describes the area of a square, f(x), in square inches, whose sides each…

A: Given function fx=x2 to find rate of change of area.

Q: Given the function h(x) = x² + 2x – 2, determine the average rate of change of the function over the…

A: Now, we are given the function : h(x)=x2+2x-2 Average rate of change of a given function f(x) over a…

Q: Use the formula below to find the instantaneous rate of change of the function at the given x-value.…

A:

Q: Find the average rate of change of the function f(x) = x2-40x+28 over the interval [10, 50].

A: topic - average rate of change of function over interval

Q: For the function g(x) = x², the average rate of change for the interval [-1, 3] is: For the function…

A: Here we have to find average rate of change of function.  The given function is g(x)=x2

Q: What is the rate of change of the function y = - 2x – 1?

A: The rate of change

Q: The function f(x) = x3 describes the volume of a cube, f(x), in cubic inches, whose length, width,…

A: Given: fx=x3,  x=5 inches

Q: Given the function h(x) = x² + 10x + 21, determine the average rate of change of the function over…

A:

Q: Given the function h(x) = x² – 8x+8, determine the average rate of change of the function over the…

A:

Q: Given the function h(x) = x² – 7x + 6, determine the average rate of change of the function over the…

A: The rate of change of a function is given by it's derivative.

Q: Given the function h(x) = x2 + 10x + 21, determine the average rate of change of the function over…

A: The objective is to determine the average rate of change of the given function.

Q: Q 4 Find the average rate of change between 5 and 0 for: f(x) = 6x2 -9x - 6

A: Obtain the average rate of change of function as follows:

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

A:

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: Given f(x) + 4x + 2, find the average rate of change on the interval [1, 3].

A:

Q: the demand x is the number of items that can be sold at a price of $p. for x = p^3 - 5p + 1300,…

A: Given that  x = p^3 - 5p + 1300  To find the rate of change with respect to x by differentiating…

Q: for the function f(x)= √2x+3, estimate the instantaneous rate of change at x=5. use h value of 0.01

A: The instantaneous rate of change of f at x = a is f'(a), if it exists,

Q: Find the average rate of change of f(x) = 7x² – 4 on the interval (3, b]. Your answer will be an…

A: Finding the average rate of a function in a given interval

Q: Find the average rate of change of f(x) = 3x2 - 2, from 2 to 4.

A:

Q: Find the average rate of change of the function f(r) = - r+ 5x + 2, from x = 2 to x = 5. Average…

A: Given that: f(x)=-x2+5x+2

Q: Given the function f(x) = –x² – 5x + 12, determine the average rate of change of the function over…

A:

Q: Determine the value of k so that the rate of change of the function f (x) = 4x² + kx – 7 is 7 when…

A: Answer

Q: Given the function f(x) = -x² – 7x + 19, determine the average rate of change of the function over…

A: Given function is: fx=-x2-7x+19 And the given interval is: -9≤x≤3 At x=-9:…

Q: Find the average rate of change of f(x) = 9x2 – 8 on the interval [2, t]. Your answer will be an…

A:

Q: Find the average rate of change of f(x)=4x^2-2 from 2 to 4 

A: For the function f(x) the rate of change in a closed interval a to b is given (f(b)-f(a))/b-a Here,…

Q: There is a bacteria cell in a Petri dish that is reproducing at a rate of              r(t) = 2t^2+1…

A: Solution:

Q: x = -t4 – 5t – 3 2.

A:

Q: The rate A (in tons per year) at which a pollutant is being dumped near a city is given by the…

A:

Q: Between 2006 and 2016, the number of applications for patents, N, grew by about 3.1% per year. That…

A: Solve the differential equation by variable separation method. Use the initial condition to…

Q: Find the average rate of change of f(x)=2x²+3x-1 from 1 to 2. -9 18 3

A:

Q: Find the average rate of change of f(x) = 7x² – 4 on the interval [3, b]. Your answer will be an…

A:

Q: Given the function f(x) = -x² – 7x + 15, determine the average rate of change of the function over…

A: Given, fx=-x2-7x+15 over the interval -9≤x≤3 To find the average rate of change.

Q: Find the average rate of change of f(x) = 3x2 +2x – 2 on the interval [2, t].

A: 555

Q: Given the function f(x) =-2x +3x-7, calculate the average rate of change on the interval [1, 1+h].

A:

Q: Find the average rate of change of f(x) = 3x2 - 5x from 1 to 3.

A: Given to evaluate the average rate of change of f(x) = 3x2 - 5x from 1 to 3.

Q: Find the derivative of the function f(x) = (2+8)2 8a2+15

A: To find: The derivative of the given function f(x).

Q: Given the function g(x) = -x2 – 3x +5, determine the average rate of change of the function over the…

A: