document.write( "Question 1075732: Let
\n" ); document.write( "f(x)={−6x^2+2x for x<0,
\n" ); document.write( "f(x)={3x^2-2 for x⩾0.
\n" ); document.write( "According to the definition of the derivative, to compute f′(0), we need to compute the left-hand limit \r
\n" ); document.write( "\n" ); document.write( "limx→0− =?\r
\n" ); document.write( "\n" ); document.write( " , which is
\n" ); document.write( "undefined
\n" ); document.write( " , \r
\n" ); document.write( "\n" ); document.write( "and the right-hand limit \r
\n" ); document.write( "\n" ); document.write( "limx→0+?\r
\n" ); document.write( "\n" ); document.write( " , which is
\n" ); document.write( "0
\n" ); document.write( " . \r
\n" ); document.write( "\n" ); document.write( "We conclude that f′(0) is
\n" ); document.write( "undefined
\n" ); document.write( " . \r
\n" ); document.write( "\n" ); document.write( "Note: If a limit or derivative is undefined, enter 'undefined' as your answer. \n" ); document.write( "

Algebra.Com's Answer #690407 by Boreal(15235) $\"\"$ $\"About$

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The right hand derivative is 6x, and at 0 the derivative is 0. Furthermore, as x approaches 0 from the right, the limit approaches 0. Answer for the right-hand limit is 0.
\n" ); document.write( "For the left hand limit, the derivative is -12x+2, and the limit is +2. As the function approaches 0 from the left, it doesn't exist at 0, but it does exist for points less than 0, and the value approaches +2.
\n" ); document.write( "Because +2 and 0 are not equal, f'(0) is undefined. \n" ); document.write( "

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