Question 1126442
<font color="black" face="times" size="3">{{{f(x)= 3x^2 +5x}}} Given function


{{{f(x)= 3(x)^2 +5(x)}}} Place parenthesis around each x. The parenthesis will help with FOIL and distributive steps later on.


{{{f(x+h)= 3(x+h)^2 +5(x+h)}}} Replace every x with x+h


{{{f(x+h)= 3(x^2+2xh+h^2) +5(x+h)}}} FOIL


{{{f(x+h)= 3x^2+6xh+3h^2 +5x+5h}}} Distribute


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{{{(f(x+h)-f(x))/(h) = (highlight(3x^2+6xh+3h^2 +5x+5h)-(highlight_green(3x^2 +5x)))/(h)}}} Stuff in red is f(x+h); stuff in green is f(x)


{{{(f(x+h)-f(x))/(h) = ((3x^2+6xh+3h^2 +5x+5h)-(3x^2 +5x))/(h)}}}


{{{(f(x+h)-f(x))/(h) = (3x^2+6xh+3h^2 +5x+5h-3x^2-5x)/(h)}}} Distribute


{{{(f(x+h)-f(x))/(h) = (6xh+3h^2+5h)/(h)}}} Combine like terms


{{{(f(x+h)-f(x))/(h) = (h(6x+3h+5))/(h)}}} Factor out h


{{{(f(x+h)-f(x))/(h) = (cross(h)(6x+3h+5))/(cross(h))}}} Divide and cancel


{{{(f(x+h)-f(x))/(h) = 6x+3h+5}}} Final Answer</font>