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Using the limit definition, how do you differentiate $f (x) = 7 x + 8$ $f(x) = 7x + 8$ ?

1 Answer

Nov 2, 2015

See the explanation section below.

Explanation:

$f (x) = 7 x + 8$ $f(x) = 7x+8$

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

$= lim_(hrarr0)([7(x+h)+8]-[7x+8])/h$

$= lim_(hrarr0)(7x+7h+8 - 7x - 8)/h$

$= lim_(hrarr0)(7h)/h$

$= lim_(hrarr0)7$

$= 7$

So, $f'(x) = 7$

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