How do I find the instantaneous velocity of a curve?

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Answer 1 · 2014-09-28T14:54:09

The instantaneous velocity is found by taking the derivative of the curve and then substituting in a value of x.

Example:

$f (x) = x^{3}$ $f(x)=x^3$

$f'(x)=3x^2$

Below are the instantaneous velocities at various values of $x$ for the curve.

$x=-3 -> f'(-3)=3(-3)^2=27$

$x=0 -> f'(0)=3(0)^2=0$

$x=1 -> f'(1)=3(1)^2=3$

$x=5 -> f'(5)=3(5)^2=75$