The difference quotient:

Will give you the rate of change for any single point difference in any function.
So you can find the quotient by letting h go towards 0 AKA the limit.
And the function you will get is the rate of change, and then just plug in a certain x-value to find the rate of change at that specific point.

Higher-Order Derivatives:
Derivatives of derivatives, you really only need second derivatives for concavity, and nothing else.
Change to a change, to a change, etc.
Also used for velocity and acceleration.

Find the equation of the tangent line:

  1. First find the derivative
  2. Plug the x value into the derivative and you get “m”
  3. Then get the point on the function (x, f(x))
  4. Then put it into the slope-intercept form.