Interpolate f(2.5) and f(11) in the following table by using an appropriate formula. x 2 4 6 8 10 y 30 40 60 85 120

Q: Find the power function f(x)= cx^k such that f(1) = 2 and f(2)=64

A: Given f(x) = cxk and we have to find the values for c and k.

Q: Based on the following table, find. f(-2) -3 -2 -1 1 2 F(x) 4 5 5 2 1.6 1.15 O 1.6 O 9 O 2

A: Here table shows the value of f(x) at given values of x

Q: Find a general formula for f (n)(x). f (x) = xe−x

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Q: Consider the following function: 3x 10z - 17 1 - 10x -1 f(x) = 17 10 2 13 1 a) What is the highest…

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Q: Find the interval(s) for which the function f (x) = 3x4 + 32x3 + 279 is increasing. O (-8, o0) O…

A: We find the critical points using f'(x)=0

Q: For the martix A= 2 5 3 4 If f(x)=x2+4, what is the answer to f(A).

A:

Q: Find f given f'(x) = x² – 6x + 6 and f(9) = 13 O f(x) = 3x - 3x? + 33 O f(x) = 2x2 – 6 + 40.5 O f(x)…

A: To find the value of f(9) we first find the value of f(x). Now given that f'(x)=x2-6x+6  ,to find…

Q: Use the below table values to approximate f' (3) using the Three - point end point formula with h= -…

A: The solution is given as

Q: Let f(x) = ax* + bx² + 50. Determine the values of a and b so that f(x) has a point of inflection at…

A: We have to find value of a and b

Q: "Find the difference quotient of f(x) = 2x +3x +1 and simplify it fully." A student attempts to…

A: Expansion of  (x+h)2 is taken wrong at 2nd step. Correction is  (x2 + h2 + 2hx) .

Q: Find the function F(x) such that F' (x) = 8x and F(0) = 1 O 1+4x^2 O 4x^2

A: topic- Functions

Q: : Find a2f and a2f of the following: дх ду ду дх (1) f(x,y) = In(x?y) + ху (2) f(x,y) = e-3x*y³ +…

A: While finding partial derivative in multivariable function, if we have to find the partial…

Q: Find f'(x) for f(x) = - 3x + 4) Do not simplify. x3 - x2 + 3x Select one: O A. 6(x3 - x2 + 3x)(3x +…

A:

Q: Find f'(a) for 9. f(z) = V6 - 4x 18 f'(a) = (-4x+6)

A: Given:         To determine: f'(x)

Q: Find (f – 9)(x) if f(x) = -3a? + 2x – 3 and g(æ) = 2x2 – 3x + 4. O (f - 9)(x) = 5x² – 5x + 7 • (f –…

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Q: Find f'(a) at the given number a.  f(x)=(6x+7)1/2 ,  a = 7

A: Use derivative

Q: Compute f '(a) algebraically for the given value of a. f(x) = 3x2 + x; a = 8 f '(a)

A: The given function is  f(x) = 3x2 +x We know that (d/dx) xn = n. xn-1

Q: Find f '(x), if f (x) = e−5x 5e O-5e^-5x 5e^-5x 5x

A:

Q: Given that f(æ) = x'h(x) h( – 1) = 2 h'( – 1) = 5 Calculate f'( – 1). Hint: Use the product rule and…

A: To find  f' (-1) =?

Q: Find the net change in f(x) on – 4.5 < x < 4.5 where: f'(x) = V81 – x2

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Q: Find a general formula for f (n)(x). f (x) = x−1/2

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Q: Differentiate the following f (x)% 3sin-(e9) %3|

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Q: The following values are obtained from the function f(x) = 2* X: 1 2 3 5 7 Ans. 15.65 f(x): 2 4 8 32…

A: Newton's divided difference formula can be defined as:…

Q: Express f(x) in the form a(x − h)2 + k. f(x) = −4x2 + 24x − 17   f(x)=?

A: Given: f(x) = −4x2 + 24x − 17…

Q: Suppose you have just finished approximating f (x) = x3 for 0 ≤ x ≤ α and ended up with φˆ(α, x) =…

A: Given suppose you have just finished approximation f(x) =x3 for 0≤x≤α and ended up with φ^ α, x=…

Q: 1 Compute and simplify the difference quotient for f(x) = V1- x

A: The given function is fx=11-x. Replace x by x+h and obtain that, fx+h=11-x+h. Obtain the difference…

Q: Use the below table values to approximate f'(3) using the Three- point end point formula with h= -1…

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Q: Complete the input-output table for f(x) = X -4 -3 -2 -1 -0.5 -0.25 0.25 0.5 1 2 3 4 5 X 5 -. If…

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Q: Let f(r) = -4(x – 2)³ + 1. Find a formula for f-1.

A: We plug f(x)=y, then switch x and y f(x)=-4(x-2)3+1 y=-4(x-2)3+1x=-4(y-2)3+1

Q: Differentiate the following function.   f(x)=9−2x+e−5x d/dx9−2x+e−5x=nothing   Enter your answer in…

A: fx=9-2x+e-5x

Q: Let f (x) = 2x – 3x + 2 and g (a) = 6x 5x +2. What is the rule for (g- f) (x)? o (g – f) (x) = 4e² –…

A: 3rd Option  is true

Q: 4. Find a formula for the inverse of f(x) = V2 – 8x.

A:

Q: Which formula is used to calculate  f(8)? f(x) = {2x+8  x5 a) x−5 / x−9 b) 2x+8 c) 7^x−9 d) x e)…

A:

Q: Compute f '(a) algebraically for the given value of a. (x) = x2 - 8; a = 9 f '(a)

A: Given : f(x) = x2-8

Q: If f(x) = 3 + 2x and g(x) = square root of 4 + 4x Then, what is the composite function of f o g?

A: Given: - The functions are, f(x)=3+2x and g(x)=4+4x To find: - The composite function of f∘g

Q: Find (f1)'(3) given the following table of values. f(z) f'(z) 3 1

A: The given table is, x fx f'x 2 3 1 This means that, At x=2,   fx=3   and  f'(x)=1. That is,…

Q: Find the range of f(x)=x-5x+6. O (-00, 1/4] O -1/4, co) O (-00, 00)

A: Range of Quadratic Functions Graphically : The range of a function y = f(x) is the set of values y…

Q: Express f(x) in the form f(x)= (X-k)qx)+r for the given value of k. f(x) = 3x + 8x3 - 10x2 + 62; k=…

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Q: zero for f(x) : = x7 - 1150 with 3, then x 2 %3D %3D 2.69009 2.70738 2.74052 2.75641 2.72419

A:

Q: Differentiate the function D = 3 – In p. - D' =

A: Simply use the standard form of derivative and calculate the differentiation.

Q: Evaluate whether the following initial values is true in the function: y=4cos(x/2)+3x² a.) when x =…

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Q: A- Find the averag value of the function f(x)=x+ B- Find the aree √x²+2x on(2,4).

A:

Q: Express f(x) in the form f(x) = (x-k)q(x) +r for the given value of k. f(x) =x° + 4x + 8x + 8, k = –…

A: We will solve the following.

Q: For the function f(x) = (E)', find f-'(x). 8 Of (x) = (8/") || 4 Of (x) = (V8x)* f1 (x) = V (8æ)“…

A: Solution: The objective is to find the inverse of the given function

Q: Given that f(x)x) h(-1) 3 Calculate f(-1) [HINT: Use the product rule and the power rule.]

A: The product rule and power rule of differentiation is shown on the board.

Q: 5. Let f(x) = ab". Determine the constant b so that f(-1) = 10 and f(2) = :.

A:

Q: Find f(5) using Newton- Gregory interpolation formula from the following table. 8 f(x) 16 Answer:…

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Q: Given that f(x) = x°h(x) h( – 1) = 5 h'(-1) = 8 Calculate f'(- 1). Hint: Use the product rule and…

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Q: Use backward-difference of ( two point formula) formula to compute f'(0.7), where h=0.1, f(0.6)=…

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