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How do you find f'(x) using the definition of a derivative for #f(x)= 5x + 9 # at x=2?

1 Answer

Oct 18, 2015

See the explanation.

Explanation:

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

#f'(x)=lim_(h->0) (5(x+h)+9-(5x+9))/h#

#f'(x)=lim_(h->0) (5x+5h+9-5x-9)/h#

#f'(x)=lim_(h->0) (5h)/h=lim_(h->0) 5 = 5#

#f'(x)=5#

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