If 8fx+6f1/x=x+5 and y=x2fx then dydx at x=−1

8fx+6f1/x=x+58f1/x+6fx=1x+5solve, we getfx=1288x−6x+10∴y=x2fx=1288x3−6x+10x2dydx=−12824x2−6+20xdydx/x=−1=−114

If 8fx+6f1/x=x+5 and y=x2fx then dydx at x=−1

8fx+6f1/x=x+58f1/x+6fx=1x+5solve, we getfx=1288x−6x+10∴y=x2fx=1288x3−6x+10x2dydx=−12824x2−6+20xdydx/x=−1=−114

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If $8 f (x) + 6 f (1 / x) = x + 5$ and $y = x^{2} f (x)$ then $\frac{d y}{d x}$ at $x = - 1$

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$\frac{1}{14}$

$- \frac{1}{14}$

answer is C.

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Detailed Solution

$8 f (x) + 6 f (1 / x) = x + 5$

$8 f (1 / x) + 6 f (x) = \frac{1}{x} + 5$ solve, we get

$f (x) = \frac{1}{28} (8 x - \frac{6}{x} + 10)$

$∴ y = x^{2} f (x) = \frac{1}{28} (8 x^{3} - 6 x + 10 x^{2})$

$\frac{d y}{d x} = - \frac{1}{28} (24 x^{2} - 6 + 20 x)$

$\frac{d y}{d x} /_{x = - 1} = - \frac{1}{14}$

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If 8fx+6f1/x=x+5 and y=x2fx then dydx at x=−1

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If $8 f (x) + 6 f (1 / x) = x + 5$ and $y = x^{2} f (x)$ then $\frac{d y}{d x}$ at $x = - 1$