How do you use the limit definition of the derivative to find the derivative of #f(x)=3x-7#?

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Answer 1 · 2016-12-15T21:34:34

# f'(x) = 3 #

The definition of the derivative of #y=f(x)# is

# f'(x)=lim_(h rarr 0) ( f(x+h)-f(x) ) / h #

So Let # f(x) = 3x-7 # then;

# \ \ \ \ \ f(x+h) = 3(x+h) -7 #
# :. f(x+h) = 3x+3h -7 #

And so the derivative of #y=f(x)# is given by:

# \ \ \ \ \ f'(x) = lim_(h rarr 0) ( (3x+3h -7) - (3x-7) ) / h #
# " " = lim_(h rarr 0) ( 3h ) / h #
# " " = lim_(h rarr 0) 3 #
# :. f'(x) = 3 #