Ilce the following table to answer the questions below. Module 6 Problem Set 1 2 3 4 f(x) f'(x) g(x) g'(x) 1 2 3 4 3 4 2 1 4 1 3 Find h'(4) if h(x) f(x) · g(x) f(x) Find h'(4) if h(x) = g(x) Round to 3 decimals as needed. Find h'(4) if h(x) = f(g(x))

Q: Find f''(x). f(x) = V (x² + 1) 5 %3D f"(x)=|

A: topic - derivative of a function

Q: If ƒ(x) ƒ'(x) = - 53 x - 7' what's f'(x)?

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Q: 10. (a) Given that f(x) = x² + 2 and g(x) find X - 3' f(8(x)) and state its domain. What is f(8(5))?…

A: 10). (a) Given function are fx=x2+2 and gx=2x-3. To find fgx and state its domain and also to find…

Q: 1. if f(x)= x2-4,  g(x)=x3 , F(x)=1/(x-3) a. F(g(y)) b. f(square root of x4+2)

A: F(g(y)) can be obtained by replacing x by g(y) in F(x)

Q: h(x)= Find f(x) such that h(x) = (fog)(x) and g(x)= 10 1-x' f(x) = 10 1-x¹0 10 4 1+x

A: We can solve this as follows:

Q: 52. f(x) = 9/x3 [1, 3]

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Q: Using the definition of the derivative, compute f'(x) for the following functions. (a) f(r) = -3 (b)…

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Q: A graphing calculator or computer algebra system is recommended. f'(x) and its graph are given. Use…

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Q: Use the following graph of y = f (x) to answer the questions. H 10- |||

A: Graphically, a function is not differentiable when there is a sharp point or there is any…

Q: Suppose that f(x) 2 4x Find f'(x).

A: use quotient rule for differentiation

Q: 1, -1 X'=1 3 0 0 2

A: The given differential equation is  dXdt=1-1-1131002X The general solution is of the form…

Q: 7. Given f(x) x + 1 write an equation for the inverse 3' function.

A: The steps to calculate the inverse is given below: Replace f(x) by y. Now replace x with y and…

Q: Find the following using the table below. x 1234 f(x) 13 4 2 f'(x) 1234 g(x) 3 12 4 g'(x) 1 2 4 3…

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Q: Question 14 (2) + h(x)]dr 8 1.5 -2/6 -7 -6 Blank 1:

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Q: dx (2x-1)3

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Q: Given that: f(-3) = 2, f'(-3) = 4, g(-3) = 9, g'(-3) = 7, calculate the following: (fg)'(-3) =…

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Q: If W = [wij ] is an n × n skew-symmetric, show that wjj = 0, for j = 1, . . . , n

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Q: Question 1 Consider the following table of values: X f(x) f'(x) g(x) g'(x) -2 -3 1 2 3 4 -5-6-7 Find…

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Q: are there any problems where (fog )(x)=(gof )(x)

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Q: Solve the problem

A: The given function is:fx=x12To find f''x

Q: By using False Position for f(x) = x3 - 4x +4 (XL=-3; xU=2) xr will replace

A: This is interesting question but before the solution we must know about the  false position method…

Q: Find f'(x). f(x) = (x² + 1) * f"(x) = %3D

A: Find f''(x)

Q: Find each of the following. In some cases, you may need to rewrite the function firs (a) F'(x) for…

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Q: Over what range of x-values can each of these equations be solved for x in terms of y? What can you…

A: The equation x^5 + x - 2 = y can be solved for x in terms of y using implicit differentiation.…

Q: 6. Given that f(x) = 3x? + 1, find +h)=[(x)

A: Given f(x)=3x2 + 1

Q: Given f(-6)= 18, f'(-6) = -16, g(-6) = -10, and g' (-6) = 14, find the value of h' (-6) based on the…

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Q: The Mean Value Theorem for problem 3 says that between x=-2 and x=2, there exists a value x=c that…

A: Let, y=f(x) =27-x2Now , f(-2) =27-(-2)2  =27-4=23   and f(2) = 27-22  =  27-4=23   and…

Q: 12. Given f(x) = 3x²+x-2, and g(x)=x-1, find the values of the following. f(1)-g(1) f(g(1)) g-¹…

A: We are given f(x)=3x2+x-2,   g(x)=x-1