document.write( "Question 1094525: If f(x)= -2/x+3, what would be the simplest form of f(x+h)-f(x)/h assuming that h ≠ 0 \n" ); document.write( "

Algebra.Com's Answer #709111 by KMST(5328) $\"\"$ $\"About$

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$\"%28f%28x%2Bh%29-f%28x%29%29%2Fh\"$ =[f(x+h)-f(x)]/h is the average rate of change of the function between $\"x\"$ and $\"x%2Bh\"$ .\r
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\n" ); document.write( "\n" ); document.write( "For $\"f%28x%29=+-2%2Fx%2B3\"$ , with $\"h%3C%3E0\"$ , it is
\n" ); document.write( " $\"%28f%28x%2Bh%29-f%28x%29%29%2Fh\"$ $\"%22=%22\"$ $\"%28-2%2F%28x%2Bh%29%2B3-%28-2%2Fx%2B3%29%29%2Fh\"$ $\"%22=%22\"$ $\"%28-2%2F%28x%2Bh%29%2B3%2B2%2Fx-3%29%2Fh\"$ $\"%22=%22\"$ $\"%28-2%2F%28x%2Bh%29%2B2%2Fx%29%2Fh\"$ $\"%22=%22\"$ $\"%28-2x%2F%28x%28x%2Bh%29%29%2B2%28x%2Bh%29%2F%28x%28x%2Bh%29%29%29%2Fh\"$ $\"%22=%22\"$ $\"%28%28-2x%2B2x%2B2h%29%2F%28x%28x%2Bh%29%29%29%2Fh\"$ $\"%22=%22\"$ $\"2h%2F%28x%28x%2Bh%29h%29\"$ $\"%22=%22\"$ $\"highlight%282%2F%28x%28x%2Bh%29%29%29\"$ $\"%22=%22\"$ $\"highlight%282%2F%28x%5E2%2Bxh%29%29\"$
\n" ); document.write( "For this problem, the meaning of \"simplest\" is whatever the teacher thinks it is.
\n" ); document.write( "As the expression $\"%28f%28x%2Bh%29-f%28x%29%29%2Fh\"$ is used to introduce the concept of derivative,
\n" ); document.write( "I would expect that $\"%28f%28x%2Bh%29-f%28x%29%29%2Fh2%2F%28x%5E2%2Bxh%29\"$ is what the teacher had in mind.
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\n" ); document.write( "NOTE: When you type expressions into a computer or calculator,
\n" ); document.write( "you should make sure you type the parentheses that were implied in those long fraction bars we can write on paper:
\n" ); document.write( " $\"%28f%28x%2Bh%29-f%28x%29%29%2Fh\"$ =[f(x+h)-f(x)]/h , but f(x+h)-f(x)/h= $\"f%28x%2Bh%29-f%28x%29%2Fh\"$ ,
\n" ); document.write( "-2/x+3= $\"-2%2Fx%2B3\"$ , and $\"-2%2F%28x%2B3%29\"$ =-2/(x+3)
\n" ); document.write( "Forgetting to type some of those parentheses implied by other grouping symbols may lead to wrong results.
\n" ); document.write( "If you type \"0.732-0.002/0.713-0.003\" into a calculator, you are likely to get
\n" ); document.write( "0.732-0.002/0.713-0.003= $\"0.732-0.002%2F0.713-0.003\"$ , and that is approximately $\"0.732-0.002805049-0.03=approximately0.7261974951\"$ ,
\n" ); document.write( "because most calculators know about order of operations.
\n" ); document.write( "If what you meant was
\n" ); document.write( "(0.732-0.002)/(0.713-0.003)= $\"%280.732-0.002%29%2F%280.713-0.003%29=0.730%2F0.710=approximately1.028169014\"$ ,
\n" ); document.write( "you got the wrong result. \n" ); document.write( "

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