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

1 Answer

Nov 2, 2015

See the explanation section below.

Explanation:

#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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