Let (x) *+1 (a) Evaluate (0), (6), and a + 6). R6) = Ra + 6) - (b) Find the domain of f. (Enter your answer using interval notation.) (c) What is the average rate of change of f between x6 andx- 107

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A: Consider the given function f(x)=−x2+4x−4

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Q: 1 Use the power rule to find the derivative of f(x) = Vx 15 f'(x) = %3D

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Q: 2) Use the limit definition to find the derivative of the given function. y = 3r2 – 2x

A: Limit definition of derivative is f'(x)=limh→0f(x+h)-f(x)h

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Q: What is the average rate of change of the function f ( x ) = 3 x over the interval [ 2 , 5 ]

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Q: What is the average rate of change of the function f(t) = -3t between t--4 and f--3?

A: what is average rate of change of the function f(t)=t2 -3t between t=-4 and t=-3   answer  put t=-4…

Q: Find the average rate of change of the function over the specified interval. f(x) = 2x2 - 3x - 4,…

A: The given function is f(x)=2x2-3x-4 ; [-2,1]

Q: Apply the second derivative test to find all relative extrema. (c) f(x) = 1

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Q: Find the approximate error, relative approximate error, and absolute relative approximate error of…

A: The approximate error is calculated using the formula: Ea=Present value-Previous value. The relative…

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A: f(x)=x3 Find f'(-4)

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Q: Find the average rate of change of the function over the interval [-2, 1] f(x) = 2.x³ – 5.x +3

A: To determine the average rate of change of the below function over the interval [-2,1]. fx=2x3−5x+3

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Q: What is the relative error in estimating the first derivative of f (z) = 25x - 6x2 + 7x- 88 at x-2,…

A: Given equation is f(x) = 25x3 - 6x2 + 7x - 88∴ f′(x) = 75x2 - 12x + 7

Q: Consider the function as folows:-   r(x) = 2x - 5 /(3x + 1)2 In general, how do you find the…

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

Q: 95. Prove that the average rate of change of the linear function f(x) = −2x + 4 on any interval I is…

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A: Given a function: f(x)= ln(x) and the function is defined in the domain x∈(0, ∞)Then, f'(x)=1x

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Q: Find the x-value for all relative extrema of f(x) using the first derivative test, and specify…

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Q: Determine the average rate of change of the function on the given interval.  f(x)= 3x2-4 on [1,2]

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Q: What is an average rate of change of function f(x) over the interval [1, 6]?

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A: The average rate of change of f(x) over an interval [a, b] is:

Q: on the interval specified. g(x) = 4x3 − 3  on  [−3, 3]

A: The average rate of change of g over the interval [-3,3] is, 36 The detailed solution is as follows…

Q: Is the function F(x) as given is constant, increasing, or decreasing on the interval (0, ∞)?…

A: Fx=∫x2x1t dt⇒Fx=lntx2x⇒Fx=ln2x-lnx⇒Fx=ln2xx          ∵lnx-lny=lnxy⇒Fx=ln2

Q: 7 Use the power rule to find the derivative of f(x) = x f'(x) =

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Q: Let f(x)= 2x^3+3x^2-12x on [1,3] What is the average rate of change in f on [1,3]?

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Q: What is the average rate of change of f between x=3 and x=10

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Q: 6. Use the difference quotient to estimate the 2 instantaneous rate of change in f(x) = x² at x=3…

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Q: Find the average rate of change of the function f(x) = x 5x - 1, over the interval [-1,3

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.