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Suppose f(r) = 3x + 4. Then the inverse of f is given by %3D f '(x) = x/3-4/3 Moreover, f'(x) = 3 vand %3D (f ")'(=) = 1/3 %3D In general, if f'(x) = A, then %3D (f ')'(f(x)) = 3A+4 V (Note: Your answer must be in terms of A.) Now let f(x) = x + x*. Then f(1) = 2 f'(1) = f '(2): 34 and

Suppose f(r) = 3x + 4. Then the inverse of f is given by %3D f '(x) = x/3-4/3 Moreover, f'(x) = 3 vand %3D (f ")'(=) = 1/3 %3D In general, if f'(x) = A, then %3D (f ')'(f(x)) = 3A+4 V (Note: Your answer must be in terms of A.) Now let f(x) = x + x*. Then f(1) = 2 f'(1) = f '(2): 34 and

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 5T
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Suppose f(r) = 3x + 4. Then the inverse of f is given by f '(x) = x/3-4/3 Moreover, f'(x) = 3 and %3D (f ')'(=) = 1/3 %3D In general, if f'(x) = A, then %3D 3A+4 V (Note: Your answer must be in terms of A.) Now let f(x) = x + x³. Then f(1) = 2 f'(1) = f '(2) 34 and (f ')'(2) = 81 Notice that you can obtain the last two results without knowing a general expression for the inverse function of f. Indeed, if you feel enterprising try to come up with such an expression.
Transcribed Image Text:Suppose f(r) = 3x + 4. Then the inverse of f is given by f '(x) = x/3-4/3 Moreover, f'(x) = 3 and %3D (f ')'(=) = 1/3 %3D In general, if f'(x) = A, then %3D 3A+4 V (Note: Your answer must be in terms of A.) Now let f(x) = x + x³. Then f(1) = 2 f'(1) = f '(2) 34 and (f ')'(2) = 81 Notice that you can obtain the last two results without knowing a general expression for the inverse function of f. Indeed, if you feel enterprising try to come up with such an expression.
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