Consider the values of f and g in the given table. f'(x) g(x) g'(x) 3 4 -3 -2 -1 -2 3 2 -4 -1 0 -3 1 2 3 4 f(x) 2 1 3 -1 Compute: f(g(x))₂-1 d dx Compute: g(f(x)),-1 d dx d Compute: f(x³ - x²) |z=2 dx Compute: (g(x)³ - g(x)²) |__2 d · dr.

Q: Find the function f (x) for which f (x) = e-5x, f (0) = 1.

A: A function is a relation which maps each value in its domain to exactly one value in its range. For…

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A: An x-intercept of a function f(x) is a point on the x-axis at which the graph of the function f(x)…

Q: Use the given graph of y = f(x) to graph the function g : g(x) = f(x + 1) + 1

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Q: Find f′(x) and f′(c). Function f(x) = (x − 4)/(x + 4) Value of c = 3

A: Now differentiating with respect to x, we get

Q: The linearization of f (x) = x² based at 3 is L (x) = [ Select ] [ Select ] (x - [ Select ] Done […

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Q: X x + 2 A1. The functions f and g are defined by f(x) (a) Calculate f'(x) and g'(x). d (b) Calculate…

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Q: Of (x) = (4x-6x* + 4 3 3 Of (x) = x* – 2x³ + 5 Of (x) = x* – x³ +4 6 ,3 %3D f (r) – 2r4 6r3 1 8

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Q: Find  f (n)(x).   f(x)  = 2x

A: Given that f(x)=2x

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A: Differentiation is the process of finding derivative or rate of change of a function. Suppose we…

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Q: Find f′′(x). f(x)=(x 2+2)9

A: Given fx=x2+29. The objective is to find f"x.

Q: 1. Use forward and backward difference approximations of O(h) and a centered difference…

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Q: Consider the following. f(x) = 8x - 3, g(x) = 1 - x The quotient of two functions, (f/g)(x), is…

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Q: 3. Let f(x) = x¹/3 and g(x) = 2x² + 5x – 1. A. Write out the equations for all four functions: ƒ(x),…

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Q: Consider the function g(x)=(f(x))^5. If f(4)=3 and f′(4)=−2, then find g′(4).

A: Given: g(x)=f(x)5f(4)=3f'(4)=-2

Q: F(x) = 2ln(x). What is F′(2)?

A: we have to find derivative of f(x) at x=2where f(x) is given by

Q: 2. (a) (5 points) Let f(x) = Vr +1 and g(x) = x² + 2x. Find (f o g)(1) and (go f)(1). %3D %3D 1+ x…

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