How do I find the instantaneous velocity of a curve?

Question

1925 views around the world

You can reuse this answer
Creative Commons License

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)=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#