00:01
In this question, we are asked to use a linear approximation to approximate the square root of 9 .1.
00:06
And we'll start with the function f of x equals to the square root of x, and we will linearize it near a equals to 9.
00:16
The reason it's 9 because it's easy to calculate f of 9 equals to the square root of 9 equals to 3.
00:27
And 9 is very close to 9 .1, right? so we should expect a good approximation.
00:40
Now we will, the linearization is going to be l of x equals to f of 9 plus f prime of 9 times x minus 9.
00:54
We already calculated f of 9, now we need to calculate f prime of 9.
00:59
To do that, we need to calculate f prime of x.
01:02
F prime of x is the derivative of the square root of x.
01:06
Another way to write square root of x is x to the 1 1 1⁄2 power.
01:11
And now we can use the power rule...