document.write( "Question 1088613: Find the gradient of the tangent where t = 3, given x=(2t-5)(t+1)^3 \n" ); document.write( "

Algebra.Com's Answer #702915 by Fombitz(32388) $\"\"$ $\"About$

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The slope(gradient) of a curve is equal to the value of the derivative at that point.
\n" ); document.write( "So using the chain rule,
\n" ); document.write( " $\"dx%2Fdt=%282t-5%293%28t%2B1%29%5E2%2B%28t%2B1%29%5E3%282%29\"$
\n" ); document.write( " $\"dx%2Fdt=%28t%2B1%29%5E2%283%282t-5%29%2B2%28t%2B1%29%29\"$
\n" ); document.write( " $\"dx%2Fdt=%28t%2B1%29%5E2%286t-15%2B2t%2B2%29\"$
\n" ); document.write( " $\"dx%2Fdt=%28t%2B1%29%5E2%288t-13%29\"$
\n" ); document.write( "So then when $\"t=3\"$ ,
\n" ); document.write( " $\"m=dx%2Fdt=%283%2B1%29%5E2%288%283%29-13%29\"$
\n" ); document.write( "Work that out for your answer.\r
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