00:01
Suppose f of x equals the square root of 1 minus x.
00:03
If we are to find the linear approximation of this function, we first want to get the derivative of f so that we can have the slope of this linear function.
00:19
Now, we have to note that l of x is equal to f prime of x sub 0 times x minus x sub 0, plus f of x of 0.
00:32
Since f prime of x equals the derivative with respect to x of 1 minus x raised to 1 half, then this is just 1 half times 1 minus x raised to negative 1 half times negative 1.
00:50
1, or that's equal to negative 1 over 2 squared of 1 minus x.
00:56
At x sub 0, which is equal to 0, we have f of x of 0, that's f of 0 equal to the square root of 1 minus 0, which is equal to 1.
01:10
And f prime of x of 0, which is f prime of 0, is equal to negative 1 over 2 times the square root of 1 minus 0, which is equal to negative 1 1 1.
01:20
So l of x is equal to negative 1 half times x minus 0 plus 1 or that's negative 1 half x plus 1...