Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following function h(x), find h' (1). Answer: h(x) = Answer: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following function h(x), find h' (1). f(x) g(x) h(x) = 2f(x) + 3g(x) f(x) + g(x)

Q: For each of the above functions, prove that f(f-1(x)) = f-1(f(x)) = f(x) = +6 f(x) = x3 + 2 f(x)…

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Q: Let f and g be functions such that f(0) = 3, g(0) = 5, f' (0) = 4, g'(0) = -3. Find h'(0) for the…

A: Given f0=3,    g0=5f'0=4,   g'0=-3hx=gxfx To find h'0

Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following…

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Q: Find all functions f(x) with the following properties. f'(x) = x +1, f(8) = 0 %3D f(x) =| %3D

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Q: Is the mathematical statement correct. If f(x)=f(-x), then f’(x)=f’(-x). Explain why

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Q: Find the function f(x) if f'(x) = ex+ 2 +(3/x) and f(1) = 6

A: We have to find the integral of f'(x) to obtain f(x) Steps: 1. Integrate with respect to x 2. Apply…

Q: Suppose g(x) = x²f(x) and it is known that f(2) = 5 and f'(2) = -2. Evaluate g'(2). g'(2) =

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Q: (A) h(x) = 12f(x). %3D h'(2) = %3D (B) h(x) = -119(r). %3D h'(2) = %3D (C) h(x) = 2f(x) + 3g(x).…

A: Given Data: f’(2)=2 g’(2)=-1 (A) h(x)=12f(x) The derivative of the given function. h'x=12f'x For…

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A: Using the given value we find the composition function value and value of f’(2)

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Q: Let f and g be the functions in the table below. N X f(x) g(x) f'(x) g'(x) 1 3 2 4 6 2 1 3 5 7 3 2 1…

A: (a)Consider, F(x)=f(f(x))Differentiate with respect to x. (Use chain rule of…

Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following…

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A: f''(x)= x(x-2)(x+1)2  To find the points of inflection of function f  A. -2 and 1 B. 2 and -1 C. 2…

Q: Let f and g be the functions in the table below. g(x) 2 3 1 X 1 2 3 f(x) 3 1 2 (a) If F(x) =…

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Q: Let f(x) : Find f'(x). (Suggestion: rewrite the function before differentiating it.) х +

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Q: 1. Assume that the function f is a one-to-one function. (a) If f(2) = 5, find f-(5). Your answer is…

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A: Given function f(x) - f(x) = x gx2To find out f'(2x), we first differentiate f(x) with respect to x,…

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