Question 551966
<pre>
First of all do NOT write <s>f(x) = [f(x+h)-f(x)]/h</s> because
f(x) = 7x² + 6x + 7.  Never write that something is equal to something
it is not equal to.  I'm sure you knew that f(x) was not equal to the
formula for the difference quotient, but what you wrote says just that.

You must write:

Difference quotient = {{{(f(x+h)-f(x))/h}}}

f(x) = 7x² + 6x + 7

First find f(x+h)

f(x+h) = 7(x+h)² + 6(x+h) + 7 = 7(x²+2h+h²) + 6x+6h + 7 = 7x²+14hx+7h²+6x+6h+7

Then

difference quotient = {{{(f(x+h)-f(x))/h}}}

Now we can substitute for both f(x+h) and f(x):

difference quotient = {{{((7x^2+14hx+7h^2+6x+6h+7)-(7x^2+6x+7))/h}}}

difference quotient = {{{(7x^2+14hx+7h^2+6x+6h+7-7x^2-6x-7)/h}}}

We cancel the terms which cancel and we have

difference quotient = {{{(cross(7x^2)+14hx+7h^2+cross(6x)+6h+cross(7)-cross(7x^2)-cross(6x)-cross(7))/h}}}

difference quotient = {{{(14hx+7h^2+6h)/h}}}
 
factor h out of the numerator:

difference quotient = {{{(h(14x+7h+6))/h}}}

Cancel the h's

difference quotient = {{{(cross(h)(14x+7h+6))/cross(h)}}}

difference quotient = 14x+7h+6

Edwin</pre>