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How do you find the instantaneous rate of change for $f(x) = 3/x$ for x=2?

1 Answer

Alan P. · David B.

Apr 26, 2016

Instantaneous rate of change for $f(x)=3/x$ at $x=2$
is $-3/4$

Explanation:

$f(x)=3/x=3*x^(-1)$

The general instantaneous rate of change is given by the derivative:
$color(white)("XXX")(d f(x))/(dx) = -3*x^(-2) = -3/(x^2)$

At $x=2$ this becomes
$color(white)("XXX")-3/(2^2) = -3/4$
graph{ (3/x-y) (3.0*x/4.0+y-3.0)=0 [-4.5,4.5,-2.2,2.7]}

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