document.write( "Question 1111998: HELPP! Using the Δ definition, show that the derivative of any linear function f(x) = Ax +B is f'(x) = A. \n" ); document.write( "
Algebra.Com's Answer #727025 by Theo(13342)![]() ![]() You can put this solution on YOUR website! the definition of derivation is f'(x) = limit of (f(x+h) - f(x)) / h, as h approaches 0.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "when f(x) = Ax + B, this becomes:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "f'(x) = limit of (A(x+h) - B - (Ax + B) / h, as h approaches 0, which becomes:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "f'(x) = limit of (Ax + Ah - B - Ax = B) / h, as h approaches 0.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Ax - Ax cancels out and B - B cancels out, so you are left with:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "f'(x) = limit of Ah / h, as h approaches 0.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "as long as h approaches 0, but is never 0, then h cancels out and you are left with:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "f'(x) = A.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "here's a reference on derivative of a function.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "http://web.mit.edu/wwmath/calculus/differentiation/definition.html \n" ); document.write( " |