Show that is linear of slope m if and only if (x h) (x) mh (for all x and h) That is to say, prove the following two statements (a) is linear of slope m implies that (x h) (x) mh (for all x and h) (b) (x h) (x) mh (for all x and h) implies that is linear of slope m ...

a First suppose fx is linear Then the slope between x fx an ...

Show that is linear of slope m if and only if (x + h) (x)

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Show that ƒ is linear of slope m if and only if ƒ(x + h) − ƒ(x) = mh (for all x and h).

That is to say, prove the following two statements:

(a) ƒ is linear of slope m implies that ƒ(x + h) − ƒ(x) = mh (for all x and h).

(b) ƒ (x + h) − ƒ(x) = mh (for all x and h) implies that ƒ is linear of slope m.

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Oct 24, 2023 05:07 AM

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Show that is linear of slope m if and only if (x + h) (x)

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Calculus

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