00:01
Okay, we have the function y equals to square root of x, and we want to find the equation of the line that is tangent to the curve, to the graph of this function at the point 1 comma 1.
00:14
So we are going to use what's called the point slope form of the equation of a line to find the equation of the tangent line.
00:23
First, since it's going to be tangent to the graph at the point 1 comma 1, we're going to label these x and y coordinates as x1.
00:32
And y1.
00:33
And the point slope form of the equation of a line learned back in algebra is y minus y1 equals m, the slope of our tangent line.
00:44
We'll talk about that in a minute times x minus x1.
00:49
So the y and the x are going to stay y and x.
00:52
The x1 and the y1, you already know their values from the coordinates of the point.
00:56
All you have to do now is find m.
00:58
M is the slope of the tangent line.
01:01
Well, the slope of the tangent line is going to be the derivative of our function at this value of x when x is 1.
01:11
So we have to find y prime.
01:15
Well, first thing i'm going to do is i'm going to rewrite our y function.
01:18
Instead of writing it as square root of x, i'm going to write it as x to the one -half power, which is equivalent to the square root of x.
01:26
And so y prime using the rules for derivatives, the power rule.
01:33
The derivative of x to the one -half is going to be one -half times x, and then we have to subtract one from this exponent.
01:42
So one -half, subtract one is negative one -half.
01:48
And so if we wanted to rewrite this a little bit neater, we could write this as one over...