Second derivative [2.4]

The derivative of $f'(x)$

• $f(x)$ - Consider some function.
• $f'(x)$ - The derivative of this function represents:
  • The instantaneous rate of change of the function at $x$
  • The slope of a tangent line to $f(x)$ at $x$
  • Has units of [units of $f$]/[units of $x$]
  • On a graph of distance traveled, $f(t)$ vs time, $t$...
    $f'(t)$ is the instantaneous velocity.
• $f''(x)$ - The second derivative of this function represents:
  • the derivative of $f'(x)$
  • the rate of change of $f'(x)$
  • the rate of change of the slope of a tangent line to $f(x)$ at $x$.
  • the slope of a tangent line to $f'(x)$ at $x$.
  • Has units of [units of $f$]/[ (units of $x$]${}^2$
  • For distance traveled, $f(t)$ vs time, $t$...
    $f''(t)$ is the instantaneous acceleration.

  2nd derivative (.ppt)