If 8 f(x)+6 f ( 1 x )=x+5 and y=x^2 f(x) , then d y d x at x=-1 equals

Step-by-step solution

aligned 8 f(x)+6 f ( 1 x ) & =x+5 y & =x^2 f(x) aligned Replace x by 1 x in Eq. (i), we obtain 8 f ( 1 x )+6 f(x)= 1 x +5 Solve Eqs. (i) and (ii) for f(x) and f ( 1 x ) Multiply by 8 in Eq. (i) and by 6 in Eq. (ii) and subtract, we get aligned & 64 f(x)-36 f(x)=8 x- 6 x +10 & 28 f(x)=8 x- 6 x +10 aligned Now, 28 x^2 f(x)=8 x^3-6 x+10 x^2 28 y=8 x^3-6 x+10 x^2 Differentiating it, aligned 28 d y d x & =24 x^2-6+20 x d y d x & = 24 x^2-6+20 x 28 ( d y d x )_ x=-1 & = 24(-1)^2-6+20(-1) 28 =- 1 14 aligned