How do you use the definition of a derivative to find the derivative of #f(x)=7x+4#?

1 Answer
Dec 6, 2016

Answer:

#f'(x)=7#

Explanation:

The derivative from #color(blue)"first principles"# is found using.

#color(red)(bar(ul(|color(white)(2/2)color(black)(f'(x)=lim_(hto0)(f(x+h)-f(x))/h)color(white)(2/2)|)))#

The aim being to eliminate h from the denominator so there is no undefined situation.

#rArrf'(x)=lim_(hto0)(7(x+h)+4-(7x+4))/h#

#=lim_(hto0)(7x+7h+4-7x-4)/h#

#=lim_(hto0)(7cancel(h))/cancel(h)=7#

#rArrf'(x)=7#