If `8f(x)+6f(1/x)=x+5` and `y=x^2(f(x),` then `(dy)/(dx)` at `x=-1` is equal to

Options

A. 0
B. `(1)/(14)`
C. `- (1)/(14)`
D. 1

Answer

C

Explanation

We have , ` 8f(x) + 6f ((1)/(x)) = x + 5 ` for all x …(i)
Therefore , ` 8f((1)/(x)) + 6f(x) = (1)/(x) + 5`
From Eqs . (i) and (ii) , we have
` f(x) = (1)/(28) (8x - (6)/(x) + 10)`
Now , ` y = x^(2) f(x) rArr y = (1)/(28) (8x^(3) - 6x + 10 x^(2))`
` rArr (dy)/(dx) = (1)/(28) (24x^(2) + 20 x - 6)`
` therefore ((dy)/(dx))_(x=-1) = (1)/(28) (24 - 20 -6) = - (1)/(14)` .