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3 12 f(x) 10 -2 Let f be a differentiable function defined on the domain a 2 -5. It is known that f is decreasing on its entire domain and has a horizontal asymptote at y = -3. Values of f() are given at select values of z in the table above. Let g be a twice-differentiable function and be defined as g(x) = | f(t)dt Let h be defined as the piecewise function h(x) = { FGr – 5) 0 -5. It is known that f is decreasing on its entire domain and has a horizontal asymptote at y = -3. Values of f(x) are given at select values of r in the table above. Let g be a twice-differentiable function and be defined as 3z2 g(x) = Let h be defined as the piecewise function h(x) = { (Gr? – 5) 0 4 (a) Find g"(x) in terms of f(x) and f'(x). (b) Explain why there is a value of c, on the interval (0, 12], such that f'(c) = -1. %3D (c) Find the value of a where g has a relative minimum. Justify. 9,

3 12 f(x) 10 -2 Let f be a differentiable function defined on the domain a 2 -5. It is known that f is decreasing on its entire domain and has a horizontal asymptote at y = -3. Values of f() are given at select values of z in the table above. Let g be a twice-differentiable function and be defined as g(x) = | f(t)dt Let h be defined as the piecewise function h(x) = { FGr – 5) 0 -5. It is known that f is decreasing on its entire domain and has a horizontal asymptote at y = -3. Values of f(x) are given at select values of r in the table above. Let g be a twice-differentiable function and be defined as 3z2 g(x) = Let h be defined as the piecewise function h(x) = { (Gr? – 5) 0 4 (a) Find g"(x) in terms of f(x) and f'(x). (b) Explain why there is a value of c, on the interval (0, 12], such that f'(c) = -1. %3D (c) Find the value of a where g has a relative minimum. Justify. 9,

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 15T
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3 12 f(x) 10 -2 Let f be a differentiable function defined on the domain a 2 -5. It is known that f is decreasing on its entire domain and has a horizontal asymptote at y = -3. Values of f() are given at select values of z in the table above. Let g be a twice-differentiable function and be defined as g(x) = | f(t)dt Let h be defined as the piecewise function h(x) = { FGr – 5) 0<r< 4 -8r + 34 a 2 4 (d) Evaluate sin(x)f'(cos(r))dr. (e) Given that f'(3) = -2, show that h is differentiable at r = 4. (f) Let k be defined as the antiderivative of f and it is known that lim k(x) = -x. Evaluate lim a)
Transcribed Image Text:3 12 f(x) 10 -2 Let f be a differentiable function defined on the domain a 2 -5. It is known that f is decreasing on its entire domain and has a horizontal asymptote at y = -3. Values of f() are given at select values of z in the table above. Let g be a twice-differentiable function and be defined as g(x) = | f(t)dt Let h be defined as the piecewise function h(x) = { FGr – 5) 0<r< 4 -8r + 34 a 2 4 (d) Evaluate sin(x)f'(cos(r))dr. (e) Given that f'(3) = -2, show that h is differentiable at r = 4. (f) Let k be defined as the antiderivative of f and it is known that lim k(x) = -x. Evaluate lim a)
12 f(x) 10 -2 AB1 Let f be a differentiable function defined on the domain r > -5. It is known that f is decreasing on its entire domain and has a horizontal asymptote at y = -3. Values of f(x) are given at select values of r in the table above. Let g be a twice-differentiable function and be defined as 3z2 g(x) = Let h be defined as the piecewise function h(x) = { (Gr? – 5) 0<r<4 -8r + 34 x > 4 (a) Find g"(x) in terms of f(x) and f'(x). (b) Explain why there is a value of c, on the interval (0, 12], such that f'(c) = -1. %3D (c) Find the value of a where g has a relative minimum. Justify. 9,
Transcribed Image Text:12 f(x) 10 -2 AB1 Let f be a differentiable function defined on the domain r > -5. It is known that f is decreasing on its entire domain and has a horizontal asymptote at y = -3. Values of f(x) are given at select values of r in the table above. Let g be a twice-differentiable function and be defined as 3z2 g(x) = Let h be defined as the piecewise function h(x) = { (Gr? – 5) 0<r<4 -8r + 34 x > 4 (a) Find g"(x) in terms of f(x) and f'(x). (b) Explain why there is a value of c, on the interval (0, 12], such that f'(c) = -1. %3D (c) Find the value of a where g has a relative minimum. Justify. 9,
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