Show that the backward difference method with extended step size h is given as follows ƒ'(x) = S(x−2h)−4ƒ (x−h)+3ƒ (x) +0(h²) 2h where O(²) is the truncation error of the approximation. State your assumption(s).

Q: Find the values of x for which  f(x)=(1/3)x3 +(5/2)x2 +6x-17 Has a tangent line that is parallel…

A: As the line is parallel, slope of them will be equal. Slope of f(x)=x33+5x22+6x-17 will be :…

Q: Show that if f (2) = −2 and f'(x) ≥ 5 forx > 2, then f (4) ≥ 8.

A: Given that f (2) = −2 and f'(x) ≥ 5. And also, f(4) ≥ 8.

Q: 9. Find a function f such that ƒ'(x) = x5 + 20 and the line 12x + y = −20 is tangent to the graph of…

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Q: Let f(x) = √6-x The slope of the tangent line to the graph of f(x) at the point (2, 2) is The…

A:

Q: Suppose f(x) f'(2) = ex x² +5 . Find:

A: Given: f(x)=exx2+5

Q: (2-9x³), find f'(x). Given f(x)= In (2-9x³), f'(x) =

A:

Q: 13. Find ƒ. (1)ƒ'(x)=x² + 3√x (2) f(t)=2cost+sec²t,-/2 <t</2,ƒ(π/3)=4; (3)ƒ*(x) = 6x+sinx.

A:

Q: Find f'(x) for f(x) = ex²+3x+¹¸

A: Given that f(x)=ex2+3x+1

Q: Let h(x)=√xf(x). If we know that f'(7) = 6ƒ(7), find a value for f(7) such that h'(7) = 4 (a) f(7):…

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Q: Let f(x) = 3e7x+3 +e². ƒ'(0) = Enter the exact value.

A:

Q: . If f(x) = V4x – 7, find f'(x).

A: we have ;  f(x)=4x-7;  we have to find f-1(x)

Q: If f(x) -6₁² = 2 f'(x) =| t³ dt then

A:

Q: Show that the third derivatives with extended step size h is given as follows: ƒ™(x) = S(x−3h)−6ƒ…

A: The given function is f(x) and the step size is h, The objective is to prove the formula…

Q: Find the tangent line to f(x)=7x4+8x−6+2xf(x)=7x4+8x−6+2x at x=−1x=−1.

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Q: If f(x) = 5x¹(²), find ƒ'(6) to 3 decimal places.

A: The given function,   f(x)=5xlnx

Q: ƒ(x, y) = x¹y — x²y³

A: Please see the below picture for detailed solution.

Q: Let f(x)=√4x² + 4x + 6 f'(x) = f'(5) =

A: To find f'(x)

Q: (8 points) Find the slope of the line tangent to the graph of 1 f (x) = 2x* – 32x + 17x2 – 9x + 4 at…

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Q: Find f. f"(x) = -2 + 36x - 12x2, f(0) = 2, f'(0) = 18

A: Given, .Given,  f(0)=2, f'(0)=18.We know,

Q: 8. Find f'(x) for (a) f(x)=(x² +3x+1)(2x+3) 2x-3x+1 (b) ƒ(x)= %3D

A: We need to find the derivative of the given functions. For (a),

Q: consider the function f(x)=x4-5x3+8x2+5x+7 compute the linear approximation Lf,1(x). Check that its…

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Q: (3) Find the equation of the line tangent to f(x)=√x atx=4

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Q: The equation of the tangent line for the function f(x) = -3 – 6x at r = 6 is %3D

A: The given function is, fx=-3-6x We need to find the equation of the tangent line to the function at…

Q: 10. Find function that satisfies the given conditions: f"(x)=6x³-3x+4, f'(1)=-3, f(1) = -6

A: The function satisfies the condition f''x=6x3-3x+4, f'(1)=-3, f(1)=-6 use the integration formulas,…

Q: - Find f (x) given f' (x) 6x2 - 4x + 3 and (2, 15) is on the curve of f (x) .

A: To find the function from derivative we need to integrate.Here we will integrate to find f

Q: Let f(x) = ƒ' (5) = f" (5) = f"" (5) = 1-4x 1+4x Compute the following.

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Q: 6. FinD F(S) if f(t)= t· cost

A:

Q: Let f(x) = 2x² 11a + 4 - The slope of the tangent line to the graph of f(x) at the point (2, 10) is…

A: This is a problem related to derivative of the function. Please follow the procedure given below.

Q: If f(t) = (t² + 3t+2) (5t² + 4), find f'(t). 201³ + 45t² + 32t Find f'(2). 40 X

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Q: 2. What is the second derivative of f(x) = - ²x³²x²+6? f"(x) = 5x² - ²³√x f"(x) = 10x + √√√x+6 a. b.…

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Q: For f(x) = x? – 2x – 1, find f(2), f'(2), and f(3) – f(2). - a. f(2) = -1 b. f'(2) = c. f(3) – f(2)

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Q: If ƒ(t) = (t² + 2t + 2) (3t² + 5), find: f’(t) = ƒ'(5) =

A: given,  f(t)=(t2+2t+2)(3t2+5)

Q: The function(x)= is concave down on which interval?

A: Given: f(x)=1x2+1