Show that g is differentiable and find

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Answered question

2022-06-19

Show that g is differentiable and find g ( x ), FTOC

Answer & Explanation

Samantha Reid

Samantha Reid

Beginner2022-06-20Added 22 answers

Let x R and choose M < x α. Then by continuity of f we have
g ( x ) = M x + α f ( t )   d t M x α f ( t )   d t ,
and so the fundamental theorem of calculus yields
g ( x ) = f ( x + α ) f ( x α ) .

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