` x= -1` पर फलन `f ( x) = 2x^(2) + 3x-5` का अवकलज ज्ञात कीजिए ।साथ ही ज्ञात कीजिए
` f'(0) + 3f'(-1) = ??`

Explanation

` f'(0) = lim _( h to 0) (f (0+h)-f(0))/h`
` = lim _( h to 0) ([2(0+h)^(2)+3(0+h)-5]-[2(0)^(2)+3(0) - 5])/h`
` = lim _( h to 0 ) (2h^(2)+3h-5+5)/h`
` = lim _( h to 0 ) (h(2h+3))/h = lim _( h to 0 )( 2h+3)`
`=3`
और `f'(-1) = lim _( h to 0 ) (f(-1+h)-f(-1))/h`
` lim _(h to 0)([2(-1+h)^(2)+3(-1+h)-5]-[2(-1)^(2)+3(-1)-5])/h`
` = lim _( h to 0 )(2(1+h^(2)-2h)-3+3h-5-2+3+5)/h`
` = lim _(hto 0 ) (2+2h^(2)-4h+3h -2)/h`
` = lim _( h to 0 )(2h^(2)-h)/h= lim_( h to0) (h(2h-1))/h`
` = lim _( h to 0)(2h-1)=-1`
बाया पक्ष : `f'(0) +3f'(-1)= 3+3(-1)`
`=3-3`
`=0`
= 0
= दाया पक्ष |