X 0 0.2 0.3 0.1 0.9048 0. 0.6073 f(x) 1 0.8187 0.7408 Find f '(x) and f "(x) at x = 0 using finite difference approximation of O(h²). (Hint: you have to choose the appropriate method based on O(h²) and the data point available).

Q: 3. Given f(r) = . Find f'(z).

A: To find the derivative of the below functions. fx=xxx

Q: Use the table below to compute h'(-1) for h(x) = f(x) g(). (E) (), (1)6 () 1/2 -2 2 1 -3 1 2 1 4. -1…

A:

Q: If f(x) + x²[f(x)]³ = 10 and f(1) = 2, find f'(1). f'(1) = -16/17

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Q: 2x2 - бх + 5 |Let f(x) = Evaluate f' (x) at x = 1. 4x2 + 3x + 10 f'(1) =

A: Given: f(x)=2x2−6x+54x2+3x+10 Quotient rule of differentiation states that ddxfg=f'g-g'fg2

Q: Find f'(x) and f"(x). f'(x) f"(x) = f(x) = (x³ + 7)ex

A:

Q: Use the table below to compute h'(2) for h(x) = 2 + 2g(x). f(1) g(x) f'(x) | g'(x) 0. 0. -2 2 1/2 -3…

A: Given query is to find the derivative of h(x) at x=2, from the given table.

Q: Let f(x) = (x³ +2x+4)* ƒ'(x) = = ƒ'(1) =

A: The function is f(x)=(x3+2x+4)4the aim is to find the derivative then the derivative of the function…

Q: 3 X 1 2 3 4 5 f'(x) 5 12 4 3 g'(x) 3 245 1 [3f(x) - 4x] x=3 =(Type an integer or a decimal.) www

A: We will find the required.

Q: 2 Find f such that f'(x) = f(9) = 20. f(x) =O

A: Topic - integration

Q: Find f such that f'(x) = f(1) = 21. f(x) =O

A:

Q: 0.6z Express the function h(x) = Ve' - 3 in the form h(x) = (ƒ o g)(x) where f(x) # x and g(x) ± x…

A:

Q: If f(1) = 4 and f '(x) ≥ 1 for 1 ≤ x ≤ 4, how small can f(4) possibly be?

A: If a function is continuous on some closed interval  and differentiable on the open interval  then…

Q: Find the following using the table below. 1 2 3 4 f(x)| 3 2 4 1 f'(x) | 1 4 3 2 9(x) 3 2 1 4 g'(x) |…

A: Solution) h ( x ) = f ( g( x ) ) h ' ( x ) = f ' ( g ( x ) ) × g ' ( x )  h ' ( 2 ) = f ' ( g ( 2 )…

Q: Consider f(x) = 3X. What is the best approximation for f'(2)?

A:

Q: Evaluate f'(x) at x =2 given f(x)= (x²– 3)“

A: The given function is fx=14x2-34. Evaluate the differential of function at x=2.

Q: Using the information in the table below, find the occupancy rate for the years 2021 to 2024 using…

A: Given α=0.3. Let At represent the actual values of the occupancy rate and Ft represent the forecast…

Q: The truncation error in calculating f '(4) for f(x) = 11x³ by using f(x+h) − f (x) approximation…

A: If f(x) = 11x3  , then,           f'(x) = 11.3x2 = 33x2 .  So, actual value of f'(4) is       f'(4)…

Q: Find f. 3 f'(x) = 1 - x? f(x) =

A:

Q: For the function f(x) = find f'"(x). Then find f''(0) and f'"(4). %3D 2+x f"(x) =] Select the…

A: We will differentiate f twice and then evaluate at x = 0 and at x = 4

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

A:

Q: The function f(æ) can be approximated by L(x) = 3 – 2(x – 4), near x = 4. What is the value of f'…

A: topic -linear approximation

Q: (vii) If f(1) = 10 and f'(x) > 2 for 1 < x < 4, how small can f(4) possibly be? Give proper…

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Q: Evaluate f'(x) at x =2 given f(x) = (x² – 3)ª A B 2 © 1 none of the given choices E 4

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Q: Use a software program or a graphing utility with matrix capabilities to write v as a linear…

A:

Q: Compute f'(a) algebraically for the given value of a. f (x) 2x – a2; a = -1 limp 0 (4 – h) = 0 limp…

A: The function is given by f(x) = 2x-x2; a =-1 To evaluate : f'(a) Formula Used : f'(a) = limh→0f(a+h)…

Q: Determine the set of values x for which the given function is differentiable. (a) f(x)=x² +4x (b)…

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Q: 03: Let S(x)=12-x-1|-1. -1. Find f"(0) and Find f'(4)

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Q: Differentiate the given function: f(x) = In(2r³ – 5æ) 6x² – 5 A f'(x) = 2x3 – 5x 1 ® f'(x) = 2x3 –…

A:

Q: True or False if f'(x) = i +t2j and f(0) = j - k then  f(x) = ti + (t3/3+1)j

A: