Calculus Power Rule word problem solved in American Sign Language
August 25, 2019
Wanna learn how to use the power rule to
solve a calculus problem? Keep watching. Hello, hello,hello!
Recently I made a video showing you how to use the power rule to calculate f ‘ x
of x. Today we are going to again discuss the power rule because we’re
gonna solve a calculus word problem. It’s gonna be fun. Are you ready? Come on. Let’s go!
Our calculus word problem uses English vocabulary “tangent to”. What does “tangent to”
mean? It means “touches at one point”. For example, if you have a line and it’s
tangent to a circle, that means that the line touches the circle at one point.
Right here. Notice that the line touches the circle twice. That means that the
line is not tangent to the circle. Notice that the line touches the
parabola at one point, right here. That means the line is tangent to the
parabola. Our calculus problem uses English words:
“derivative” I sign it as “f prime of x” and “power rule”. Here’s how I sign the
power rule. If you want to learn more about either of those two concepts, watch
another video up there on the right hand side of your screen. Now our calculus
problem: Find the equation of the line tangent to the parabola y=x^2 at the point (1, 1). We will draw a picture to help us better understand how
to solve the problem. First draw the parabola y=x^2. And here it is. Second, remember the problem says that the line touches
the parabola at the coordinates (1,1). We must find the coordinates (1, 1). Third, draw the line. Now we have a line touching the parabola y=x^2 at the point (1,1). The drawings are all finished. Now what are we going to do? We’re going to solve the problem. We’re going to have to find the
equation for this line. How do you calculate the equation of a line? Well
let’s step back a bit. Remember in algebra class there was two pieces of
information that you needed if you wanted to calculate the equation for a
line. You must know one point. We must know one point. Well yeah, we do it’s (1 ,1). We must
know the slope. We don’t know the slope of this line. How are we going to
calculate the slope? I know. We must calculate f prime of x because f prime
of x allows us to calculate the slope on any point of the line. How are we going
to calculate f prime of x? This parabola y=x^2 is a polynomial.
That means we can use the power rule. The power rule allows us to calculate f
prime of x with three easy steps. First multiply the power 2 with the
coefficient 1. 2 x 1=2. Notice that x
squared equals one x squared. I wrote one x squared because I wanted all of you to
see that this one over here is the coefficient. Bring down the X. Third, subtract 1 from the power 2. 2-1=1. Of course, x to the first power equals x. f ‘(x)=2x. Now we know two things
about this line: we know that the slope is 2 and we know that there’s one
point with the coordinates (1, 1). Now we can calculate the equation for the line. How are we going to do that? We’re going
to use the slope-intercept formula. Remember algebra class? Remember how to use y=mx+b? Now “m” represents the slope, and ‘b” represents the
y-intercept. Now what are we going to do? The “m” is going to become a 2. We must calculate ‘b” by replacing the x
and the y. The x becomes a 1 and the y becomes a 1 as well. 2 x 1=2. Bring down the “b”.
2 – 2 on the right side and 1 – 2 on the left side. 2-2=0. And bring
down the “b”. 1 – 2=-1 b+ 0=b Now what is this “b” going to become? -1. And what is the answer? y=2x -1. Thank you for watching! Hope you enjoyed
the video. Now watch more math videos!