How do you use the limit definition of the derivative to find the derivative of #f(x)=7x+1#?

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Answer 1 · 2016-07-28T21:04:42

#f'(x) = 7#

Ok we know from the power rule that we expect #f'(x) = 7# this allows us to check that we've got the answer correct.

#f'(x) = lim_(hrarr0) (f(x+h) - f(x))/h#

#=lim_(hrarr0)(7(x+h) + 1 - (7x+1))/h#

#=lim_(hrarr0) (7x+7h+1 - 7x - 1)/h = lim_(hrarr0) (7h)/h = lim_(hrarr0)7 = 7#

This is what we expected.