00:01
In order to solve this problem, we just have to take the derivative of f of x to find f prime of x, substitute in our a value, which is two into both of those, and then plug those values along with our a valued, right x minus a part, into our l of x, or our linear approximation equation, and that is all we got to do.
00:18
So let's start by taking the derivative of f of x.
00:22
So power rule on the x cubed, it leaves us with 3x squared.
00:25
Because you move the 3 to the front of the in front of the x and subtract the power by 1.
00:33
So giving us 3x squared.
00:36
The derivative of something times x is just that something.
00:41
So in this case, it's 5.
00:43
And then the last term goes to 0 because it's just a constant.
00:47
Now let's plug in our a values into both f of x and f prime of x...