document.write( "Question 151684: For the function f(x)=x^2-8, construct and simplify the difference
\n" ); document.write( "quotient f(h+h)-f(x)/h
\n" ); document.write( "The difference quotient is= \n" ); document.write( "
Algebra.Com's Answer #111496 by nabla(475)\"\" \"About 
You can put this solution on YOUR website!
This is an essential component to finding the derivative of a rational function in calculus. If you continue in mathematics you will see right away that the \"difference quotient\" must be 2x+h.\r
\n" ); document.write( "\n" ); document.write( "In any case, here it is worked out:
\n" ); document.write( "FIRST, IDENTIFY the components:
\n" ); document.write( "f(x+h)=(x+h)^2-8
\n" ); document.write( "f(x)=x^2-8\r
\n" ); document.write( "\n" ); document.write( "Now, we can just substitute these into the expression:\r
\n" ); document.write( "\n" ); document.write( "(f(x+h)-f(x))/h=(\"%28%28x%2Bh%29%5E2-8%29-%28x%5E2-8%29%29%2Fh+\")/h=\"%28x%5E2%2B2xh%2Bh%5E2-8-x%5E2%2B8%29%2Fh\"=\"%282xh%2Bh%5E2%29%2Fh\"=\"2x%2Bh\"\r
\n" ); document.write( "\n" ); document.write( "That is the answer. In calculus, we would take the limit as h goes to zero. If h is 0, 2x+h=2x. This gives the derivative of the function f(x)=x^2+c, c arbitrary. I hope you find that information interesting.
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