Problem 4: Given the function /(x) = 4x -x+1. (a) Find the average rate of change of f(x) with respect to x over the interval 0 (b) Find the instantaneous rate of change of f(x) at x-- and compare with the average rate found in (a).

Q: In Example 6 in this section, we were given f(x) = 3x2 + 2x + 11 and found f '(x) = 6x + 2. (a)Find…

A: We have to given that f(x)=3x2+2x+11 and f'(x)=6x+2. It is known that rate of change is given as…

Q: of two observat

A: Let the Geometric mean of two observations is  1n. GM=1nHM To prove that  (1+1-n²) :(1-1- n²)

Q: #7. Find the average rate of change of the function between the give values of x. y = -5x – x2…

A: The average rate of change of a function fx on an interval a, b is given by…

Q: Find the instantaneous rate of change Of the function at the Speciried value of X flx)=X?-2; X -3

A:

Q: If f is the (constant) focal length of a convex lens and an object is placed at a distance p from…

A: We have, f is the focal length (constant) of a convex lens and an object is placed at a distance p…

Q: (b) Find the instantaneous rate of change of g with respect to x at x = 3, or state that it does not…

A: 3. given graph of function is                                                       Also,…

Q: Question 1. Find the average rate of change of the function f(x) = x² – 5 on the interval [2, 2 +…

A: WE HAVE TO FIND THE AVERAGE RATE OF CHANGE OF A FUNCTION   given function is f(x)=x2-5   Given…

Q: We are given f(x) = 9x2 and f '(x) = 18x. Find the instantaneous rate of change of f(x) at x = 2.

A: Given function is

Q: 1 1. Given that y =- a. Find the average rate of change of y with respect to x over the interval…

A:

Q: The rate of growth of a population P is given by dP/dt=kP + N  where N is a constant representing…

A: Given:- The rate of growth of a population P is given by dP/dt=kP + N where N is a constant…

Q: It is known that the population of a certain country at time t is proportional to the people living…

A:

Q: 1. Explain two different ways to solve for the derivative of s(0) = 200sin cose

A: The given function is : s(θ)=200sinθcosθ We need to find the derivative in two ways.

Q: In Problems 41–44, find the average rate of change of f from 0 to π/641. f(x) = tan x 42. f(x) = sec…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: 1. f(x) =In (ta n"x)

A: Given query is to find the first derivative of the expression.

Q: 4. Find an equation of the tangent line to the graph of f(x) = ln(x ^2 + 4) at the point (2, ln(8))

A:

Q: Given the function f(x)= X x-2’ a. Determine the average rate of change on the interval -4≤x≤-1. b.…

A:

Q: 1. The number of a certain type of bacteria increases continuously at a rate proportional to the…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: A Cepheid variable star is a star whose brightness alternately increases and decreases. For a…

A: Given: A Cepheid variable star is a star whose brightness alternately increases and decreases. For a…

Q: 1. let s(x) = 1.1 Find the average rate of change of s(x) with respect to x as x changes from…

A:

Q: Question 14 ▼ Submit Question Find the average rate of change of g(x) = 3x² - 4 between the points…

A:

Q: tan(Cx) Va6+2 find the rate of change of P with respect to x, where C is a Given that P = constant.

A:

Q: Question 28 to determine the instantaneous rate of change of 3, to the nearest tenth.…

A: Explanation of the answer is as follows

Q: I6 y= tex find dy dox

A:

Q: Question 26 Calculate the average rate of change for the function f(x) = 2x² − 3x + 5 1 over the…

A:

Q: If f(x) = cos(2x), which of the equations below describes the average rate of change of f(x) over…

A:

Q: Problem 4. Find a derivative A) Vy = xy+ cos y and %3D

A: The given function is y=xy+cosy

Q: If f is the focal length of a convex lens and an object is placed at a distance p from the lens,…

A:

Q: Find the rate of change of x with respect to p. 500 – X 0 < x < 500 8x

A:

Q: 2 Refer to the graph above and without making any computa- tions find: The average rate of change…

A:

Q: Consider the function Y3x2-6×+ス a. Find the slope of the tangent lihe to the curve at x=2 be Find…

A:

Q: Find the average rate of change of y with respect to x in the interval from x=5 to x=6 and the…

A: We have to find the following conditions

Q: x3+6x-2 dx x4+6x2

A:

Q: Suppose that f(x) = 3x² – 3. (A) Find the slope of the line tangent to f(x) at x = 5. (B) Find the…

A: We find f'(x) using the power rule Slope of the line tangent to f(x) at x=5 is given by f'(5) So to…

Q: If f is the (constant) focal length of a convex lens and an object is placed at a distance p from…

A: Given,1f=1p+1qwhere f is focal lenrth and an object is placed at a distance p from the lens and its…

Q: A radioactive substance is decaying at a rate represented by y = h(t) = Rọa“, in millirems per hour.…

A:

Q: Suppose that the yield (measured in kg/ ha) of an agricultural crop is represented by the function…

A: We need to find rate.

Q: Two substances, A and B, are being converted into a single compound C. In the laboratory it has been…

A:

Q: -4 to x = 1 Find the average rate of change of g(x) = 3x° - 1 from z =

A: Average is (g(1) -g(-4)) /5

Q: he given problem. 1. For y-ln2x, determine the equation of a tangent line parallel to 2x- 3y+1-0.

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Suppose that the marginal propensity to consume is dC -0.2y = 0.8 - e dy (in billions of dollars)

A:

Q: A radioactive element decays according to the function Q= Qn e", where Q, is the amount of the…

A: Given that a radioactive element decays according to the function Q=Q0ert, where Q0is the amount of…

Q: (4) Consider the constant rate of decrease of a certain microorganism. At the start, there are…

A: We have to find the number of microorganisms that will be there after 45 seconds.

Q: If the rate of change of y with respect to x is equals to 2-y and y=8 and x=0. Find y when x=ln(2).

A: Given: The rate of change of y with respect to x  is equal to 2-y. That is, dydx=2-y

Q: QUESTION 1 Find the average rate of change from x = -4 to x = 0 for g(x) = -2x + 18. QUESTION 2…

A: The average Rate of change of function f(x) over the interval [a,b] is  =(f(b)-f(a))/(b-a)

Q: When the interest on an investment is compounded continuously, the investment grows at a rate that…

A:

Q: Question 12 Find the 2nd derivative (y") of y=√x ln x In 2

A: