00:01
Hello, welcome to this lesson.
00:03
In this lesson we will determine the slope of the tangent line to each of the curve at the given value of x.
00:10
So the first one we have y which is equal to 3 squared at x equals negative 2.
00:16
So we simply let f of x be equals to y and as such we have f of x which is equals to 3 squared.
00:27
Alright, so the slope of the tangent line is equals to the first derivative of f of x and that is equals to 6x.
00:40
Alright, so at x equals negative 2 we have f prime of x now which is negative 2.
00:52
So f prime of negative 2 which is equals to 6 times negative 2 which is equals to negative 12.
01:00
So therefore the slope is negative 12.
01:07
The slope of the tangent line to the curve is equals negative 12.
01:12
Let's go to the b part where we have y equals to x squared minus x.
01:21
So y is equals to x squared minus x at x equals to 3.
01:30
Alright, so with this we let f of x be equals to y and as such we have f of x which is equals to x squared minus x.
01:41
So the first derivative which is the slope this will be equals to 2x minus 1...