How do you find the instantaneous slope of $y=1/x$ at x=4?

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Answer 1 · 2016-11-04T15:10:18

$-1/16$

The instantaneous slope is determined by differentiating $y$ at $x=4$

Differentiating $y$ is computed by applying the quotient rule
$color(blue)((u/v)'=(u'v-v'u)/v^2$

$y=1/x$

$y'=color(blue)((1'xxx-x'xx1)/x^2)$

$y'=0-1/x^2$

$y'=-1/x^2$
$y'_((x=4))=-1/4^2=-1/16$

Therefore, the slope of y at $x=4$ is $-1/16$

How do you find the instantaneous slope of y=1/xy=1/x at x=4?