2. Suppose f (x) is a function whose domain is all real numbers, which satisfies the formula: f (x + y) = f (x) (sin (y) + 1) for any numbers x and y. (a) Show that f (x) is differentiable for all real numbers, and f' (x) = ƒ (x) for any x. (b) Can you think of an example of f (x) that satisfies the formula?

2. Suppose f (x) is a function whose domain is all real numbers, which satisfies the formula: f (x + y) = f (x) (sin (y) + 1) for any numbers x and y. (a) Show that f (x) is differentiable for all real numbers, and f' (x) = ƒ (x) for any x. (b) Can you think of an example of f (x) that satisfies the formula?

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

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