document.write( "Question 1021849: Using differentiation, estimate how much the function
\n" ); document.write( "f(x)= ax + bln(x)\r
\n" ); document.write( "\n" ); document.write( "increases by, to 2 decimal places, when a = 85 and b = 19, if x increases from 89 to 89.8 \n" ); document.write( "

Algebra.Com's Answer #637562 by robertb(5830) $\"\"$ $\"About$

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For sufficiently small enough h, f'(x) is very close to $\"%28f%28x%2Bh%29+-+f%28x%29%29%2Fh\"$ \r
\n" ); document.write( "\n" ); document.write( "==> hf'(x) is very close to f(x+h)-f(x)\r
\n" ); document.write( "\n" ); document.write( "==> 0.8*f'(89) is very close to f(89.8) - f(89).\r
\n" ); document.write( "\n" ); document.write( "Now f'(x) = $\"85%2B19%2Fx\"$ if f(x) = $\"85x%2B19lnx\"$ \r
\n" ); document.write( "\n" ); document.write( "This means the difference is approximately equal to hf'(x) = 0.8*(85+19/89) = $\"highlight%2868.17%29\"$ . \n" ); document.write( "

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