Suppose that the function f has the same average rate of change c between any two points. (a) Find the average rate of change of f between the points a and x to show that c = x) – f(a) X - a The rate of change between any two points is (b) Rearrange the equation in part (a) to show that f(x) = cx + (f(a) - ca). Multiplying the equation in part(a) by x – a, we obtain f(x) - f(a) Rearranging and adding f(a) to both sides, we have (10) - f(x) = cx + as desired. How does this show that f is a linear function? What is the slope, and what is the y-intercept? Because this equation is of form f(x) = Ax + B with constants A = and B = f(a) - , it represents a linear function with slope and y-intercept f(a) -

Q: Find the derivative of the function. A) f(x) = In(x*Vx² - 3)

A: This problem can be solved by using the Chain rule as explained in step 2.

Q: Show both the Newton and Leibniz notation for finding the derivative of y = f(x) = 4x5.

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Q: Find the derivative of the function. f(x) = ex In(x³) f'(x) = X

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Q: What is the average rate of change of the function f(x): = x² between x = -3 and x = 3?

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Q: 5. Find the derivative by using the quotient rule. 3x - 2 (a) 2x +3 V+2 (c)- 3+2x (b) x +1 x+2 (d):

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Q: 1. Find the derivative of f(x). 3x³ 2x²-x-5 - (a) f(x) = √x (b) f(x) =

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Q: Find the instantaneous rate of change of the function at the given value f(x)=6x2-4x+3; x=2

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Q: a. Suppose that Miller Corporation can produce 3500 refrigerators when the number of hours of…

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Q: Find the average rate of change of g(x) = 4x + 2 between the points (-3,-10) and (3,14)

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Q: Find the derivative of the function. f(x) = 2x In(x) f'(x) =

A: Let us consider the given function as: fx=2xlnx By using product Rule of derivative, we get:…

Q: Suppose that a company can produce 12,000 units when the number of hours of skilled labor y and…

A: Given that a company can produce 12,000 units when the number of hours of skilled labor y and…

Q: Find the derivative of the function. y In x2+9

A: Given function is: According to chain rule of derivatives:According to the quotient rule:

Q: Find the derivative of the function. h(x) = (4/x^2)+(6/x^3)

A:

Q: 1. Find the slope of the line tangent to the graph of the function defined by f(x) = 4 + 2x - x2 at…

A: As you mentioned only 1 solved

Q: Find the derivative of the function. f(x) = (x2 + 3) In(x) f'(x)

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Q: if f(x)=17x^2-x^3   , what is the rate of change of f’(x) at (-1,18)?

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Q: Calculate the derivative of f1 (x) = (2x + 3) / (x - 5) using the definition of the limit of the…

A: To find- derivative of the given function using definition  of limit.

Q: Find the instantaneous rate of change for the function at the given value. f(x)=x2+4x at x=-4

A: The instantaneous rate of change of a function at a point can be evaluated first by finding the…

Q: 16. Use the limit definition of the derivative to find the instantaneous rate of change for the…

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Q: Find the average rate of change of f(x) = 8x2 - x:(a) From 1 to 2       (b) From 0 to 1     (c) From…

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Q: Calculate the derivative of f1 (x) = (2x + 3) / (x - 5) using the definition of the limit of the…

A: (1) Given function is f1x=2x+3x−5 We have to find the derivative of f1x by using definition of the…

Q: Find the average rate of change of h1x2 = x2 - 2x + 3:(a) From - 1 to 1(b) From 0 to 2(c) From 2 to…

A: Since it is known that the average rate of change can be calculated using the formula…

Q: when you have f(x) = x^2 + 7x +10 / x^2 - 7x +6 what is the average rate of change of the function…

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Q: Find the derivative of the function. y = x2 In x2

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Q: a) calculate the derivative of: f1(x) = 2x4 - 3x3 + ½x2 + 3 b) Calculate the equation of the line…

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Q: 3- Suppose a student carrying a flu virus returns to an isolated college campus of 8000 students. If…

A: let the number of students infected is x, therefore, the number of students not infected is 8000-x…

Q: Find the average rate of change of f(x) = 3x2 - x from x1 = -1 to x2 = 2.

A: The given function is fx=3x2-x.

Q: Estimate the instantaneous rate of change of f(x) = -3x + 2 at x = -2.

A: The instantaneous rate of change of a function f(x) is the first derivative of a given function and…

Q: Find the derivative of the function g(x) = (3x² + 3x)e" = (æ),6

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Q: If f(x) = x-2 x² +4 then what is the derivative of fat x=2?

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Q: Find the derivative of the function. f(x) = In x+ 2 f'(x) =

A: We have to find the derivative of the given function.

Q: Find the derivative of the function. g(x) = In(x – 5.1x=1) g'(x) =

A:

Q: What is the instantaneous rate of change of the function f ( x ) = 5 /x  at x = 3 ?

A: Given,        The instantaneous rate of change of the function fx=5x at x=3.We know that,…

Q: Suppose a student is a carrier of the flu virus and returns to his isolated campus of 1000 students.…

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Q: 9

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Q: Find the derivative of the function. f(x) = (x² + 8) In(x) f'(x) =

A: In this question we need to find a derivative of the given function

Q: A group of survivors on a supply run has returned to their base camp with a population of 2000. Two…

A: Given:  y       = present number of infected people 2000 = total population  y'(t)  = rate of spread…

Q: Find the average rate of change of g(æ) = 2x² + on the interval [-2,3]

A: Given

Q: 5. f(x) = [(x + 5)5 – 1]4

A:

Q: Determine the instantaneous rate of change of the function f(x) x4 at the point where x = -2.

A: instantaneous rate of change of a function is differentiation of function at that point

Q: QUESTION 1 Compute the average rate of change of the function, f(x)=7x-6x - 4860 -, over the…

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Q: (2x-6) ¹² 3. h(x)= (3 + نمو)

A: The objective of the question is evaluate the derivative of the given function.

Q: Find the derivative of the function: f(x)=ln  (x-3)^2÷(2x-1)^3

A: Given function is,

Q: Suppose total cost in dollars from the production of x printers is given byC(x) = 0.0001x3 + 0.005x2…

A: average rate of change of cost between point [a,b] is given by

Q: Solve for the derivative of the function using chain rule. 6. f(x)= cot(6x3+5)

A: Derivative

Q: Let g(x)=7arctan(5x). What is the instantaneous rate of change of g(x) when x=2?

A: g(x)=7arctan(5x) to find rate differentiate g(x) with respect to x

Q: Find the average rate of change of the function between the given values of X.  y=-5x-x^2 between…

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Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

A: Given,          The total cost in dollars from the production of x printers is given by…

Q: Find the derivative of the function g(x) 4+ 2x = (x),6

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Q: Find a function with the given derivative whose graph passes through point P f'(x)=x-4, p(1,7)

A: Integrating on both sides, we get