Roboguru

Sebuah perusahaan semen dalam waktu  tahun memperoleh keuntungan total sebesar  (dalam ratusan ribu). Berapa laju keuntungan sesaat (keuntungan marginal) saat ?

Pertanyaan

Sebuah perusahaan semen dalam waktu begin mathsize 14px style t end style tahun memperoleh keuntungan total sebesar begin mathsize 14px style L left parenthesis t right parenthesis equals 1500 t squared end style (dalam ratusan ribu). Berapa laju keuntungan sesaat (keuntungan marginal) saat begin mathsize 14px style t equals 5 end style?

  1. begin mathsize 14px style.... end style 

  2. undefined 

Pembahasan Video:

Pembahasan Soal:

 begin mathsize 14px style L left parenthesis t right parenthesis equals 1500 t squared end style 

Keuntungan  marginal saat begin mathsize 14px style t equals 5 end style adalah:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as h rightwards arrow 0 of fraction numerator f left parenthesis t plus h right parenthesis minus f left parenthesis t right parenthesis over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator left square bracket 1.500 times left parenthesis t plus h right parenthesis squared right square bracket minus left square bracket 1.500 times left parenthesis t right parenthesis squared right square bracket over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator left square bracket 1.500 times left parenthesis 5 plus h right parenthesis squared right square bracket minus left square bracket 1.500 times left parenthesis 5 right parenthesis squared right square bracket over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator left square bracket 1.500 times left parenthesis 25 plus 10 h plus h squared right parenthesis right square bracket minus left square bracket 1.500 times left parenthesis 25 right parenthesis right square bracket over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator left square bracket 37.500 plus 15.000 h plus 1.500 h squared right square bracket minus left square bracket 37.500 right square bracket over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 1.500 h squared plus 15.000 h over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of left parenthesis 1.500 h plus 15.000 right parenthesis end cell row blank equals cell 1.500 times left parenthesis 0 right parenthesis plus 15.000 end cell row blank equals cell 15.000 end cell row blank blank blank end table end style 

Jadi, keuntungan marginal perusahaan semen tersebut adalah begin mathsize 14px style open parentheses 15.000 close parentheses end style ratusan ribu/tahun.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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