document.write( "Question 68783: I don't understand how to find the 'difference quotient'. Could you please help me?
\n" ); document.write( "The problem is:
\n" ); document.write( "f(x)= xｲ + 1
\n" ); document.write( "Thanks. \n" ); document.write( "

Algebra.Com's Answer #48965 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

I don't understand how to find the \r\n" );
document.write( "'difference quotient'. Could you please help me?\r\n" );
document.write( "The problem is:\r\n" );
document.write( "\r\n" );
document.write( "                       f(x) = xｲ + 1 \r\n" );
document.write( "\r\n" );
document.write( "Learn the difference quotient formula:\r\n" );
document.write( "\r\n" );
document.write( "                                f(x + h) - f(x)\r\n" );
document.write( "difference quotient formula =  覧覧覧覧覧覧覧覧予r\n" );
document.write( "                                       h\r\n" );
document.write( "\r\n" );
document.write( "First find f(x + h).  Start with:\r\n" );
document.write( "\r\n" );
document.write( "      f(x) = xｲ + 1  \r\n" );
document.write( "\r\n" );
document.write( "Replace both x's by (x + h) :\r\n" );
document.write( "\r\n" );
document.write( "  f(x + h) = (x + h)ｲ + 1\r\n" );
document.write( "\r\n" );
document.write( "Simplify the right side.  To square a binomial\r\n" );
document.write( "multiply it by itself:\r\n" );
document.write( "\r\n" );
document.write( "  f(x + h) = (x + h)(x + h) + 1\r\n" );
document.write( "\r\n" );
document.write( "Use FOIL:\r\n" );
document.write( "\r\n" );
document.write( "  f(x + h) = xｲ + hx + hx + hｲ + 1 \r\n" );
document.write( "\r\n" );
document.write( "Combine like terms:\r\n" );
document.write( "\r\n" );
document.write( "  f(x + h) = xｲ + 2hx + hｲ + 1\r\n" );
document.write( "\r\n" );
document.write( "Now substitute the following two into \r\n" );
document.write( "the numerator of the difference quotient formula:\r\n" );
document.write( "\r\n" );
document.write( "  f(x + h) = (xｲ + 2hx + hｲ + 1)\r\n" );
document.write( "      f(x) = (xｲ + 1)\r\n" );
document.write( "\r\n" );
document.write( "                                f(x + h) - f(x)\r\n" );
document.write( "difference quotient formula =  覧覧覧覧覧覧覧覧予r\n" );
document.write( "                                       h\r\n" );
document.write( "\r\n" );
document.write( "Substituting into that numerator:\r\n" );
document.write( "\r\n" );
document.write( "                         (xｲ + 2hx + hｲ + 1) - (xｲ + 1)  \r\n" );
document.write( "difference quotient  =  覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧\r\n" );
document.write( "                                       h\r\n" );
document.write( "\r\n" );
document.write( "Remove parentheses in the numerator:\r\n" );
document.write( "\r\n" );
document.write( "                          xｲ + 2hx + hｲ + 1 - xｲ - 1  \r\n" );
document.write( "difference quotient  =  覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧\r\n" );
document.write( "                                       h\r\n" );
document.write( "\r\n" );
document.write( "The xｲ and the -xｲ cancel.  The +1 and the -1 cancel,\r\n" );
document.write( "so we have:\r\n" );
document.write( "\r\n" );
document.write( "                         2hx + hｲ   \r\n" );
document.write( "difference quotient  =  覧覧覧覧予r\n" );
document.write( "                            h\r\n" );
document.write( "\r\n" );
document.write( "Factor h out of the numerator:\r\n" );
document.write( "\r\n" );
document.write( "                         h(2x + h)   \r\n" );
document.write( "difference quotient  =  覧覧覧覧覧予r\n" );
document.write( "                             h\r\n" );
document.write( "\r\n" );
document.write( "Cancel the h's\r\n" );
document.write( "                         1\r\n" );
document.write( "                         h(2x + h)   \r\n" );
document.write( "difference quotient  =  覧覧覧覧覧予r\n" );
document.write( "                             h\r\n" );
document.write( "                             1\r\n" );
document.write( "\r\n" );
document.write( "difference quotient = 2x + h\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "

\n" );