I'm having a hard time understanding what this study question is asking...   "If you can’t find instantaneous rates of change by using algebra because both the denominator and numerator will equal zero at a giving point, why can you take the derivative of a function?"

Q: A research group using hospital records developed an approximate mathematical model relating…

A: The rate of change of y with respect to (w.r.t.) is given by derivative of y w.r.t. x i.e., dydx.

Q: A regression of the LDL cholesterol level on the Body Mass Index (BMI) is shown below:LDL…

A: According to the provided information, regression line of the LDL cholesterol level on the Body Mass…

Q: Find the derivative of function f given by S(1) = =! X-1 3 x+3'

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Q: What is the set of points for which the rate of change of z is

A: Given equation - z = x2+y2           ............(1)dtRate at which x is increasing = dxdt = 2…

Q: 1. If y = x³ + x - 5 then what is the derivative of y with respect to x?

A: Derivative of a function

Q: | In Problems 50–51, explain what is wrong with the state- ment. 51. The derivative of f(x) = r° is…

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Q: Determine whether each of the following statements is true or false, and explain why In a related…

A: Suppose we have two variables x and y (in most problems the letters will be different, but for now…

Q: Suppose you know that the point (2, 3) lies on the function h. The average rate of change on the…

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Q: Can the average rate of change of an increasing function ever be negative?

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Q: Question 1 Find the average rate of change of g(x) = 5x³-2 from z = -1 to z = 4.

A: Given the query is to find the the average rate of change for the function.

Q: If the national debt of a country (in trillions of dollars) t years from now is given by the…

A: Given data:   The expression for the national debt of a country is N(t)=0.5+1.5e0.0t. The given time…

Q: Daily crude oil production by one particular oil company for 2008-2013 could be approximated by…

A: Given,          Daily crude oil production by one particular oil company for 2008-2013 could be…

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: Question 5 Determine the derivative of the given function: y = 5-2 Oy = 5"-2 (In 5)(x - 2) Oy = 5-2…

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Q: During the real estate run-up in 2000-2008, the percentage of mortgages issued in a country that…

A: The required graph is as follows: The maximum value occurs at the point 6.39507,1.59824 .

Q: What is the millionth derivative of f(x) = e x ?

A: ex

Q: The fungus Fusarium exosporium infects a field of flax plants through the roots and causes the…

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Q: Question 11 What is the derivative of y =V x3 -2x² +x -2,

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Q: If x is measured in months where x=0 represents January of 2000, and F(x) represents the US GDP…

A: given GDP is measured in  millions of dollars  x is measured in months

Q: e. Suppose someone claims that C'(5000) = -0.1. What would the practical mean- ing of this…

A: We have to find the meaning of C'(2000).

Q: Use Definition 1 or 2 to find the instantaneous rate of change of the function at the given value…

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Q: You invest some money in the stock market at time t = 0 months. If f(t), measured in dollars per…

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Q: Question #3) Hypothetical Story Line One of your friends just joined the banking sector in the…

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Q: (6) Find the direction and magnitude of the greatest rate of change of T at (3 -) 2)

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Q: 4) Find the third derivative of g(x) = e*.

A: We will solve the problem

Q: find the first derivative of   F(x) = e(x+5)

A: Given,

Q: The number of per capita cumulative cases of COVID-19 in a particular country can be modeled by g(t)…

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Q: - 5 then what is the derivative of y with respect to x?

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Q: Find the relative rate of change of f(x) at the indicated value of x. f(x)=39; x=100

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Q: Outside of the box question: The number of treated mosquitoes increased from 20 to 2000 within 8…

A: Rate of change of mosquitoes

Q: the instantaneous weight growth rate at week 16 greater or smaller or the same than the average rate…

A: Given query is to provide information regarding instantaneous rate of change and average rate of…

Q: A. Find the derivative of the given function at a given number 1. y =3x -2 at f(1)

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

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Q: QUESTION 4 The average rate of change of a function over an interval is the same as the…

A: The average rate of change is defined as ravg=fb-fab-aover same interval a,b

Q: Estimate the instantaneous rate of change of f(x) = 4. at the point a = -1 x - 6 Your answer should…

A: We need to find the instantaneous rate of change of f(x) = 4/(x-6) at x=-1.  Now,…

Q: Suppose that the spread of a disease through the student body at an isolated college campus can be…

A: Here we have to find out rate of change of y.

Q: Question 9 > Find the average rate of change of g(x) = 2x + 9. on the interval [-2,3]

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Q: O What is the geometric interpretotron of the derivative f'(a)?

A: Considering a function f(x) which is continuous and differentiable on a particular interval, then at…

Q: Suppose a block of metal heated to 250°F and then brought into a room that is at 90 ° F at 5 pm. At…

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Q: Prove that the relative rate of change 1/f(x)is negative that of f(x). Give a general formula for…

A: The relative rate of change of a function f(x) is the ratio of its derivative to itself. R(f(x)) =…

Q: The graph of a function is shown together with the tangent line at a point P. y 5 4 3 2 1 2 3 4 6. 7…

A: topic- tangent

Q: Monday, 1) Find the derivative of the given function with respects to e y = 3lan® In 3

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Q: 9. One ship is approaching a port from the east, traveling west at 15 miles per hour, and is…

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Q: (n2 – 1)* 31. H (r) = (2г + 1)8

A: In the question it is asked to calculate the derivative of H(r)=(r2-1)3(2r+1)5 using chain rule.

Q: Find f’ (x), i.e. the first derivative of the question below f (x) = (x - 4) (x – 1)

A: Topic:- derivatives

Q: (a) Find the derivative of the function f(x) = ex-1

A: Note: As per company policy we are supposed to solve only one question. So, kindly repost other…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: