Suppose F and G are continuously differentiable functions defined on [a, b] such that F'(x) = G'(x) for all x € [a, b]. Using the fundamental theorem of calculus, show that F and G differ by a constant. That is, show that there exists a CR such that F(x) G(x) = C (Remark: This is justifying the "rule" of adding a constant ff + C to indefinite inte- gration when you are computing an antiderivative. Make sure to use the right form of the fundamental theorem of calculus.)

Suppose F and G are continuously differentiable functions defined on [a, b] such that F'(x) = G'(x) for all x € [a, b]. Using the fundamental theorem of calculus, show that F and G differ by a constant. That is, show that there exists a CR such that F(x) G(x) = C (Remark: This is justifying the "rule" of adding a constant ff + C to indefinite inte- gration when you are computing an antiderivative. Make sure to use the right form of the fundamental theorem of calculus.)

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.2: Derivatives Of Products And Quotients

Problem 36E

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