8) Use the table to answer the following questions. Show work. 1 2 3 4 f(x) f'(x) 4 1 3 4 3 1 а) Find (f-1)'(3). b) Find (f-1)'F(3)).

Q: 1. Find derivative of given function defined as follows. 7-29-22 y = (8x²-3x³) ³

A:

Q: 20. The fourth derivative of y = Jx -1 is 8 D.-은(x-1) 2 16 15 A. -(x – 1) В.- С.- 8. (X - 16 M| 00

A: This question is related to differentiation, we will use basic differention rules and results to…

Q: 2. Find the derivative of a function at a certain number using the formula. f(x) – f(xo) f'(x) = lim…

A:

Q: 9. Find the first derivative: f(x) = 3ex %3D x2 (x+1)

A: Derivative of function

Q: What is the first derivative of the following function: f(x) = (x³ + 2)4 O f'(x) = 12x²(x³ + 2)³ O…

A:

Q: 3. Given f(x) = x + 2 and ƒ '(x) = give the equation of the tangent line to %3| 2Vx(x+2)² f(x) when…

A:

Q: • Show that both of the functions f(x) = (x − 1)^4 and g(x) = x^3 −3x^2 + 3x+ 2 have stationary…

A: given functions fx=x-14gx=x3-3x2+3x+2 (A) to show both have stationary point at x=1 differentiate…

Q: 4) Calculate the first derivative of the following functions: 1. f(x) = In 2x2+1° 2. f(x) =…

A:

Q: 5. Find the derivative of the function. f(x) = x°/1- 8x x(16-136x) 2/1-Sr x'(16+136x) f (x)3D 2/1-8x…

A: The function is given by,

Q: If f'(x) = 3+ 4x and the curve f(x) passes through the point (1, 8) i) Find f(x) ii) Find the local…

A:

Q: The derivative of the function f is defined by ƒ'(x) = (x² + 1) cos (x²). If f(1) = 1, what is the…

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Q: Find the derivative of the following using First Principle. 4) y = -2x2 + 3x – 12 5) f(x) = x2 + 15x…

A:

Q: What is the derivative of f(x) = %3D (² - (z – 1)")* 02 (2 – (a – 1)°) (-3z² + 8z – 3) O2 (2² - (2 –…

A:

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)f(x) whose second derivative is f′′(x)=9x+10sin(x). If f(0)=3f(0)=3 and…

A: We have to find f(x) and find f(3) using given intial condition

Q: 4. Given f (x )=x'-12x +1. Use the second derivative test to determine the local extremum off (x).

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 4)* Find the derivative of f(x)= Arcsecr. %3D f'(x) = 4 rv.r* O None of the above O Option 4 f"(x)=:…

A:

Q: 3. Let f(x) =x In(x – 3)+5. Find the equation of the line tangent to the graph of f at the point…

A: Given thatf(x)=xln(x2-3)+5f'(x)=ddxxln(x2-3)+5         =xddxln(x2-3)+ln(x2-3)ddx(x)+ddx(5)…

Q: 5 .Let f(x) =x² -e*. Find the value of x for which the second derivative s"»equals zero. 2

A:

Q: Find the fourth derivative of ƒ (z) = 4z" f(4) (z) =

A: We can make it easier for you

Q: 5. y = x3 – x²Cos(x)+ 2xSin(x) + 2Cos(x) -

A:

Q: 6. Find [ f(x)dx if f(x) = et -1, if -3<x<0 V9-x², if 0<x<3

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Q: 55. By normalizing the function f(x)==-defined in the domain [0, 2], we will get as a result the…

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Q: OFind the derivative of the 1 +5 (a). f(z) = %3D T2-5

A: As per the guidelines we can solve only one question at a time so if you need more answers then…

Q: Q:1 Find the second derivative of f(x) = 2x5 - 3VX7 at x = 1 rounded to five decimal places.

A: To find the second derivative of  f(x)=2x⁵-3x7/3 at x=1

Q: 1 6. Find the derivative of f(x)= 1 at the point 8, Vx+1

A: Given

Q: b) Use the definition of the derivative to compute f'(x) for 1)f(x) = 2v-5x + 9, 2)f(x) = x sin 3x…

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Q: The derivative of f(x) = 9z3 12 8. is %3D 3z f'(x) O f(r) – 9x?+ 12x 4 – 9r– 12x + 8e 7 O f(r) - 9x…

A:

Q: 2.) f(x) = (x5 – 2x³ + 1) 3

A:

Q: 5х f(x) = 2) Find the first derivative given that J2x+3

A: Solved below...

Q: #4) Given the function f (x) =x³-x² +2x- 1. Use the second derivative test, where applicable, to…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 2. Given f(x) = x³ – 2x² + x + 2, find x e (-1, 3) such that f'(x) = 5. 3. Compute the derivative of…

A: Since you have posted multiple questions, as per our guidelines we are allowed to answer the first…

Q: 1. Use the definition of derivative to find f'(1) 2r2 b) f(x) = Vx

A: Derivative of the function using definition

Q: If f (x) = In (4a + 1), then its third derivative is f(3) (æ) = %3D

A: In this question, concept of derivative is applied. Derivative The derivative expresses the rate of…

Q: 10. Find the particular antiderivative of the derivative f'(x) = 3x-1 – x-2 where f(1) = 5.

A:

Q: 3. Find the first derivative of the function f(x)= 2x3-4x+1 using forward Difference formula if, X1…

A: Solution:

Q: 2. Find the derivative of (a) f(x) = x* + 4x 2 + 4e" (b) f(x) = 2 tan (x) – 6"

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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: 5* The derivative of the function: f(x)= 5* + 7 7.5 In5 (5* – 7)2 7(5 In5) (5 + 7) 7(5*ln5) (5* +…

A: According to the problem, we have

Q: 7. Find the derivative of the given function. Simplify and express the answer using positi exponents…

A:

Q: 2. Using the definition of derivative, prove the following: 1 (a) f^(x)= if f(x) = Vx %3D

A: fx=x3

Q: 15. Find the linearization of f(x) = vx +1 at a = 15 and use it to find an approxima- cion to v15…

A: Given: f(x)=x+1 at a=15

Q: 11. Use the definition of the derivative to find f'(x) for the function f(x) = x2 + x + 2. Show your…

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

Q: 6.) Find the derivative of the fonction 2 8- g'cx) =

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Q: 10 The derivative of the function f(x) = x7 + - 10 726 + (r³) 10 71° + (2) 1 10 7x + 10 10 726 (z²)…

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Q: 2. Find the derivative of (a) f(x) = x* + 3x 2+ 4e" 4 (b) f(x) = 2 tan(x)- 2"

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 5. Find a function f(x) whose derivative is f'(x) = +1. (Hint: (x + 1)/x=1+1/x)

A: 5) derivative of a function is given, to find the function we have to find the anti derivative of…

Q: 2. Determine the true error and the relative true error of the first derivative of f(x) = 2.5-* %3D…

A: Solution is below

Q: 2. Consider the function f(x) = e¯*. -2x (a) Show that the derivative is f'(x) = %3D

A:

Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

A:

Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.