00:01
We want to take the first and second derivatives of the function, g of t is equal to t squared times 3t plus 1 to the 4th.
00:09
Because we never know what the first derivative of function will look like, when trying to find the second derivative, you need to be prepared to take any sort of derivative.
00:16
So let's do a quick recap on what derivatives are.
00:18
Remember that the derivative is the rate of change, and some examples of typical derivatives you might take are derivatives of a polynomial of x or power of x, so ddxxxx2x, derivatives involving the product rule, derivatives involving the chain rule, etc.
00:31
In this case, g of t equals t squared times 3 t plus 1 to 4th.
00:35
We're going to have to use both the product and change to solve.
00:37
So first we'll solve for the first derivative, and then we'll re -derive that to obtain the second derivative...