Pertanyaan

Gradien garis singgung fungsi kuadrat di titik adalah ….

$begin mathsize 14px style fraction numerator 2 x subscript 1 superscript 3 plus 2 over denominator x subscript 1 superscript 4 end fraction end style$
$begin mathsize 14px style fraction numerator 2 x subscript 1 superscript 4 plus 2 over denominator x subscript 1 superscript 3 end fraction end style$
$begin mathsize 14px style fraction numerator 2 x subscript 1 superscript 3 minus 2 over denominator x subscript 1 superscript 3 end fraction end style$
$begin mathsize 14px style fraction numerator 2 x subscript 1 superscript 3 minus 2 over denominator x subscript 1 superscript 4 end fraction end style$
$begin mathsize 14px style fraction numerator 2 x subscript 1 superscript 4 minus 2 over denominator x subscript 1 superscript 3 end fraction end style$

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Jawaban terverifikasi

Pembahasan

Ingat bahwa gradien garis singgung fungsi pada titik dengan absis adalah Misalkan maka Perhatikan bahwa dan Jadi, Maka, jawaban yang tepat adalah B.

Ingat bahwa gradien garis singgung fungsi pada titik dengan absis adalah

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell m subscript g s end subscript end cell equals cell limit as h rightwards arrow 0 of invisible function application fraction numerator f open parentheses x subscript 1 plus h close parentheses minus f open parentheses x subscript 1 close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of invisible function application fraction numerator open parentheses open parentheses x subscript 1 plus h close parentheses squared minus open parentheses x subscript 1 plus h close parentheses to the power of negative 2 end exponent close parentheses minus open parentheses open parentheses x subscript 1 close parentheses squared minus open parentheses x subscript 1 close parentheses to the power of negative 2 end exponent close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of invisible function application fraction numerator open parentheses open parentheses x subscript 1 plus h close parentheses squared minus 1 over open parentheses x subscript 1 plus h close parentheses squared close parentheses minus open parentheses x subscript 1 superscript 2 minus fraction numerator 1 over denominator x subscript 1 superscript 2 end fraction blank close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of invisible function application fraction numerator open parentheses x subscript 1 plus h close parentheses squared minus 1 over open parentheses x subscript 1 plus h close parentheses squared minus x subscript 1 superscript 2 plus fraction numerator 1 over denominator x subscript 1 superscript 2 end fraction over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of invisible function application fraction numerator open parentheses open parentheses x subscript 1 plus h close parentheses squared minus x subscript 1 superscript 2 close parentheses minus open parentheses 1 over open parentheses x subscript 1 plus h close parentheses squared minus fraction numerator 1 over denominator x subscript 1 superscript 2 end fraction close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of invisible function application fraction numerator open parentheses open parentheses x subscript 1 plus h close parentheses squared minus x subscript 1 superscript 2 close parentheses over denominator h end fraction minus limit as h rightwards arrow 0 of invisible function application fraction numerator open parentheses 1 over open parentheses x subscript 1 plus h close parentheses squared minus fraction numerator 1 over denominator x subscript 1 superscript 2 end fraction close parentheses over denominator h end fraction end cell end table end style$

Misalkan

maka

Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row P equals cell limit as h rightwards arrow 0 of invisible function application fraction numerator open parentheses open parentheses x subscript 1 plus h close parentheses squared minus x subscript 1 superscript 2 close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of invisible function application fraction numerator open parentheses x subscript 1 superscript 2 plus 2 x subscript 1 superscript blank h plus h squared minus x subscript 1 superscript 2 close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of invisible function application fraction numerator open parentheses 2 x subscript 1 h plus h squared close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of invisible function application 2 x subscript 1 plus h end cell row blank equals cell 2 x subscript 1 plus 0 end cell row blank equals cell 2 x subscript 1 end cell end table end style$

dan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row Q equals cell limit as h rightwards arrow 0 of invisible function application fraction numerator open parentheses 1 over open parentheses x subscript 1 plus h close parentheses squared minus fraction numerator 1 over denominator x subscript 1 superscript 2 end fraction close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of invisible function application fraction numerator open parentheses fraction numerator x subscript 1 superscript 2 minus open parentheses x subscript 1 plus h close parentheses squared over denominator open parentheses x subscript 1 plus h close parentheses squared x subscript 1 superscript 2 end fraction close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of invisible function application fraction numerator x subscript 1 superscript 2 minus open parentheses x subscript 1 plus h close parentheses squared over denominator h open parentheses x subscript 1 plus h close parentheses squared x subscript 1 superscript 2 end fraction end cell row blank equals cell limit as h rightwards arrow 0 of invisible function application fraction numerator x subscript 1 superscript 2 minus open parentheses x subscript 1 superscript 2 plus 2 x subscript 1 h plus h squared close parentheses over denominator h open parentheses x subscript 1 plus h close parentheses squared x subscript 1 superscript 2 end fraction end cell row blank equals cell limit as h rightwards arrow 0 of invisible function application fraction numerator negative 2 x subscript 1 h minus h squared over denominator h open parentheses x subscript 1 plus h close parentheses squared x subscript 1 superscript 2 end fraction end cell row blank equals cell limit as h rightwards arrow 0 of invisible function application fraction numerator h open parentheses negative 2 x subscript 1 minus h close parentheses over denominator h open parentheses x subscript 1 plus h close parentheses squared x subscript 1 superscript 2 end fraction end cell row blank equals cell limit as h rightwards arrow 0 of invisible function application fraction numerator negative 2 x subscript 1 minus h over denominator open parentheses x subscript 1 plus h close parentheses squared x subscript 1 superscript 2 end fraction end cell row blank equals cell fraction numerator negative 2 x subscript 1 minus 0 over denominator open parentheses x subscript 1 plus 0 close parentheses squared x subscript 1 superscript 2 end fraction end cell row blank equals cell fraction numerator negative 2 x subscript 1 over denominator open parentheses x subscript 1 close parentheses squared x subscript 1 superscript 2 end fraction end cell row blank equals cell fraction numerator negative 2 x subscript 1 over denominator x subscript 1 superscript 4 end fraction end cell row blank equals cell fraction numerator negative 2 over denominator x subscript 1 superscript 3 end fraction end cell end table end style$

Jadi,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell m subscript g s end subscript end cell equals cell P minus Q end cell row blank equals cell 2 x subscript 1 minus fraction numerator negative 2 over denominator x subscript 1 superscript 3 end fraction end cell row blank equals cell 2 x subscript 1 plus fraction numerator 2 over denominator x subscript 1 superscript 3 end fraction end cell row blank equals cell fraction numerator 2 x subscript 1 superscript 4 plus 2 over denominator x subscript 1 superscript 3 end fraction end cell end table end style$

Maka, jawaban yang tepat adalah B.

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