Find the average rate of change of the function f(x) 2x2 2x- 2, on the interval x E [2,4]. Average rate of change = Give exact answer!

Q: Consider the two functions fz) = 5x +5 and g(x) = 5x² - 5. a. Determine the instantaneous rate of…

A: rate of change means differentiate with respect to x so differentiate it f'(x) = 10x g'(x) = 10x   a…

Q: Estimate the instantaneous rate of change of the function f(x)=−x2+4x−4 at x=1 using the average…

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

Q: Find the derivative of the functionf(x) = Vx – 2. Provide your answer below: f'(x) =O

A: We have to find derivative

Q: Use the second derivative test to find the extreme values of the function J () = x³ – su² 24X .

A:

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: Find the absolute extrema of the function f(x) = (x + 16) 1/3 on the interval[-5,2]. Find the second…

A: To find  The absolute extremum of the given function.

Q: Find the average rate of change of f(x) with respect to x on the interval. f(x)= x^2 -5x+1; [-3,0]

A: f(x)=x2-5x+1;-3,0 We need to find the average rate change of f(x)

Q: Find the average rate of change of the function between the given values of x. y = −5x − x2 between…

A: The given function y and the values of x between which the average rate of change of y is to be…

Q: II. Obtain the required order or level of derivative. 1. y = 3x5 + 4x³ – 4x + 1, find y" 2. f(x)…

A: Solve differentiate

Q: Find the second derivative [ f"(x)] of the given function: f(x) = eln Vx²+2 %3D (x2 + 2)) x(x² + 2)-…

A: Given problem:- Find the second derivative [f''(x)] of the given function:   f(x) = eln√(x^2+2)

Q: Consider the function f (x) = x2. Calculate the rate of change of f (x) at x = 1, and compare your…

A: Consider the function f (x) = x2  To Calculate the rate of change of f (x) at x = 1.

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

A: We will find the average rate of change of the function.  We know,  the average rate of change =…

Q: Find the derivative

A: The first derivative of f(x) is represented byf'(x) and the second derivative is represented by…

Q: Let f be the function given by f(x)=x^3−2x^2+5x−16. For what value of x in the closed interval [0,5]…

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Q: Find the derivative of the function g(x) g'(x) = ex + 3xe (2+3x)² = x| X et 2 + 3x

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Q: Find the relative extrema using both the first and second derivative tests. f(r) = 2x³ – 9x² + 12x.…

A: Consider: fx=2x3-9x2+12x. Critical point is the point where the derivative of the function is either…

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

Q: Find the relative extrema of f (x) = 7+ 144x – 9x? using both first %3D and second derivative tests.…

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Q: Find the second derivative. 1 h(x) = x2 %3D | h"(x) = %3D

A:

Q: Find the average rate of change of g(x)=−5x^3+4 from x=−3 to x=3

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: Find the relative extrema of f(x) = 8+72x – 9x? using both first and second derivative tests. f (x)…

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Q: a) Find the derivative of g(x) = 3tanx – 4cotx. %3D b) What is the value of g 3.

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Q: Find the derivative of the function f(x) = x2 - 5x + 3 at the numbers (a) 2 and (b) a. %3D

A: a. From the definition we have the following, Simplify further,

Q: Let f(x) = (x² + 3x)e*. Determine the value of the third derivative of f(x) for x = 0.

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Q: Assume a function such that Y = (2x410)/(6x² + 5x). Obtain the first derivative. O f'(X) = (8x³ -…

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Q: Find the average velocity of the function over the given interval. y= - 3x? - x, [5,6] – X,

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Q: V². Find the derivative of f(x) = In x² +1 %3D x(2r - 1)2

A: Derivative: f(x)=lnx2+1x(2x3-1)2ln(mn)=ln m-ln nln(x2+1)=12ln(x2+1)

Q: (5) Find the local maximum and minimum values of f(r) = 1+3x2 – 2.r using either the First…

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Q: 6. Find the second derivative, f"(x). (6) = f(x)

A: To find  The second derivative of f(x).

Q: Find the average rate of change of the function from x, to x,. Function x-Values f(x) = x² – 3x + 8…

A: The given function and x -values are: fx=x2-3x+8, x1=1, x2=5 Now, calculate the average rate of…

Q: Find the average rate of change of f(x)=x2−x+2 on the interval [1,t].

A: To find the average rate of change of function

Q: Find the derivative: n[(x³ + 2) (x² + 3)]. Evaluate S dx. Зx8 — 2 2x*- x2 Evaluate dx.

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Q: Find the first derivative of the function * 4 f (x) = Væ + 4

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Q: Find the relative extrema of f(x) = 9 + 30x – 5x? using both first and second derivative tests. f(x)…

A: Derivative one time and equate it to zero to find the critical point. Derivative second to find the…

Q: Given the function f(x) = – x° – 6x2 + 5x + 12 , use either the First Derivative Test OR the %3D -…

A:

Q: Find the absolute extrema of the function f(x) = (x2 + 18)273 on the interval[-4,3]. Find the second…

A:

Q: f y=x^2(e^x)

A: Derivative: ddx(u.v)=u.dvdx+v.dudxy=x2(ex)Here u=x2,v=ex

Q: Find the inflection points of the function f(x) = x 2 ln x

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Q: Differentiate the function below y = ln ( ( etan x √(x2 +1) )  /  (x-3)5)

A: We first simplify the given function.  y=lnetanxx2+1(x-3)5y=ln(etanx)+lnx2+1-ln(x-3)5  [addition and…

Q: Find the relative extrema of f(x) = 2+ 90r 5x using both first and second derivative tests. f(x) has…

A: We can find the relative extremum as below

Q: Differentiate the functions: 1. y = 3x – Vx 2. y = 2 – 3x – 3. Given the function f(x) = x³ – 5x +…

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Q: What is the average rate of change of f(X)= X2-2 on the interval [-1,3]?

A:

Q: Determine the n-th derivative fn) of the function f: (0, +0) → R, f(x) = x ' exp ( 1 - ), n EN

A: f(x)=1x,  f:(0, +∞)→R,…

Q: Find the derivative of the function. f(x) = /7+ V5+ VI f '(x) = %3D

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Q: find the derivative of the function  F(x)= e^x/e^x + 8

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Q: Find the derivative of the function. f(x) = /2 + V1+ Va 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: Find the average rate of change of the function f(x) = = læ + 0x + 8, on the interval x E [-2,0].…

A: Given:fx=x2+8  on the    interval -2,0Average rate of change of the functionAx=fb-fab-aa=-2 , b=0

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

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Exponential Growth Model

The relation that represents an exponential function is: