00:01
In this question, we are told that the tangent line to the graph of y equals to f of x at the point 9 negative 7 passes through the point negative 9 negative 7.
00:10
And we are asked to find f of 9 and f prime of 9.
00:14
The general formula for the tangent line is y minus y0 equals to f prime of x not times x minus x not.
00:27
This is a general formula for the tangent line at the point of x not.
00:34
X0 y0.
00:36
In our case the tangent line is at the point 9 negative 7, which means that x not equals to 9 and y0 equals to negative 7.
00:47
On the other hand, y not equals to f of x not and since x not equals to 9, y not equals to f of 9.
00:59
And that's exactly what we are asked to find in the first part.
01:03
And this means that we are all we are already given f of 9.
01:10
F of 9 equals to y0 equals to negative 7.
01:20
So we answer the first part of the question.
01:22
Now we need to calculate f prime of 9...