Given #f(x) = 3x^2+6x#, what is #(f(x+h)-f(x))/h# ?

1 Answer
George C.
Nov 3, 2016

#(f(x+h)-f(x))/h = 6x+6+3h#

Explanation:

#f(x) = 3x^2+6x#

#f(x+h) = 3(x+h)^2+6(x+h)#

#color(white)(f(x+h)) = 3(x^2+2hx+h^2)+6(x+h)#

#color(white)(f(x+h)) = (3x^2+6hx+3h^2)+(6x+6h)#

#color(white)(f(x+h)) = (3x^2+6x) + 6hx+3h^2+6h#

#color(white)(f(x+h)) = f(x) + 6hx+6h+3h^2#

So:

#(f(x+h)-f(x))/h = (6hx+6h+3h^2)/h = 6x+6+3h#

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