Dengan menggunakan konsep limit fungsi, tentukan gradien garis singgung fungsi berikut. f(x)=3x2−2x+1

Pertanyaan

Dengan menggunakan konsep limit fungsi, tentukan gradien garis singgung fungsi berikut.

$\style{font-size:14px}{f(x)=3x^2-2x+1}$

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

Gradien garis singgung fungsi dengan menggunakan konsep limit fungsi adalah

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell m subscript A end cell equals cell limit as h rightwards arrow 0 of fraction numerator f open parentheses x plus h close parentheses minus f open parentheses x close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator open square brackets 3 open parentheses x plus h close parentheses squared minus 2 open parentheses x plus h close parentheses plus 1 close square brackets minus open square brackets 3 x squared minus 2 x plus 1 close square brackets over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 3 open parentheses x squared plus 2 x h plus h squared close parentheses minus 2 open parentheses x plus h close parentheses plus 1 minus open parentheses 3 x squared minus 2 x plus 1 close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 3 x squared plus 6 x h plus 3 h squared minus 2 x minus 2 h plus 1 minus 3 x squared plus 2 x minus 1 over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 6 x h plus 3 h squared minus 2 h over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of 6 x plus 3 h minus 2 end cell row blank equals cell 6 x plus 3 times open parentheses 0 close parentheses minus 2 end cell row blank equals cell 6 x minus 2 end cell end table end style$

maka gradien garis singgungnya adalah .