## Comparison of a function, its First Derivative, and its Second Derivative

Click the play button to see the function, its first derivative, and its second derivative in succession. Use the Pause button to slow think through each step before the next derivative is shown.

Then, using the Input window, enter a new function for f(x).
Use ^ for exponents:  for example f(x) = x^5 + x^3 + 1  represents  f(x) = x5 + x3 + 1
If you click the buttons for g(x) and h(x) before entering f(x), you will not automatically see the derivatives.  Then you can click them again after you have considered how they will look.

Note:  You can copy/paste the equation from here to the input box below:  f(x) = x^5 + x^3 + 1
Also a couple of others:  f(x)=sin(x)           or     f(x)=e^x             or      f(x)=e^(-x)
(For function involving e, click both g(x) and h(x) in the algebra window to see how they overlap when graphed.)
Be sure to try one that you think of, or one from the homework on derivatives.

Can you anticipate what the derivative of a function will look like?  (Hint:  Think about the slope of the tangent line.)

G. Battaly, Math Department, Westchester Community College, See Calc Pages , Created with GeoGebra