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Chapter 4: Q. 1 (page 403)

Fill in the blanks to complete each of the following theorem statements:

If Fand Gare _____ functions, then F'(x)=G'(x)if and only if G(x)= _____.

Short Answer

Expert verified

If F and G are differentiable functions, then F'(x)=G'(x ) if and only ifG(x)=F(x)+c

Step by step solution

01

Step 1. Given Information

A theorem statement is given with blanks we have to fill the blanks with correct answers.

The given statement with blanks is:

If F and G are ____ functions, then F'(x)=G'(x ) if and only if G(x) = _____.

02

Step 2. Theorem statement

Functions with the Same Derivative Differ by a Constant Theorem:

If F and G are differentiable functions, then F'(x)=G'(x)if and only if F(x)=G(x)+cfor some constant c.

Therefore the blanks are Differentiable andG(x)=F(x)+c.

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