### Home > APCALC > Chapter 10 > Lesson 10.1.7 > Problem 10-83

10-83.

By now you are comfortable with the graphical implications of the first and second derivatives of a function. gives you the slope of the tangent line at a point while

*tells you the concavity of the graph at a point. There is nothing to stop us from finding the third and fourth (and beyond!) derivatives, although there are not any significant graphical characteristics associated with higher derivatives.*

*is simply the rate of change of*

*and so on.*

What is

if?Take the derivative four times.

If

, write an expression for thederivative,.Take a few derivatives of this function and look for patterns.