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.

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