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If `8f(x)+6f(1/x)=x+5`and `y=x^2(f(x),`then `(dy)/(dx)`at `x=-1`is equal to0 (b) `1/(14)`(c) `-1/4`(d) None of these |
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Answer» Correct Answer - C We have , `8f(x)+6f((1)/(x))=x+5` for all x Therefore , `8f((1)/(x))+6f(x)=(1)/(x)+5` From Eqs.(i) and (ii) , we get `f(x)=(1)/(28)(8x-(6)/(x)+10)` Now , `y=x^2f(x)` `rArr y=(1)/(28)(8x^3-6x+10x^2)` `rArr (dy)/(dx)=(1)/(28)(24x^2+20x-6)` `therefore ((dy)/(dx))_(x=-1)=(1)/(28)(24-20-6)` `=-(1)/(14)` . |
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