document.write( "Question 254184: Determine the slope of the tangent to y=1/1-x at the point (2,-1) without constructing a table. Explain what you are doing. \n" ); document.write( "

Algebra.Com's Answer #186507 by drk(1908) $\"\"$ $\"About$

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The question was
\n" ); document.write( "Determine the slope of the tangent to y=1/(1-x) at the point (2,-1) without constructing a table.
\n" ); document.write( "step 1 - take the derivative of the function. We use the quotient rule to get
\n" ); document.write( "(i) $\"%28%281-x%29%2A0+-+1%2A%28-1%29%29+%2F+%281-x%29%5E2\"$
\n" ); document.write( "and then
\n" ); document.write( "(ii) $\"1+%2F+%281-x%29%5E2\"$
\n" ); document.write( "Now put two into (ii) to get the slope at 2. We get
\n" ); document.write( "(ii) $\"1+%2F+%281-2%29%5E2\"$ = 1.
\n" ); document.write( "So slope = 1 and passes through (2,-1)
\n" ); document.write( "Y = mx + b
\n" ); document.write( "-1 = 2*1 + b
\n" ); document.write( "b = -3.
\n" ); document.write( "answer:
\n" ); document.write( "Y = 2x - 3. \n" ); document.write( "

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