Can't see the pic but, pythag
Find the rate of change of the distance between the origin and a moving point on the graph of y = x² + 1 if dx/dt = 2 cm/sec.
Here's the solution:
except I don't understand where they got that first equation D = √(x² + y²)
can somebody please explain..?
here's a working link to the solution if you want to look:
Also, how would I do this problem if instead of y = x² + 1, it's y = sin x?
"D" represents the distance from the origin to the moving point. That's why you use the Pythagorean theorem:
I made you a picture:
Since you already know that , you can plug it in for "y" in the equation ----->
From there, take the derivative of D. As you know, the derivative of that equation is
Since you know that , you can just plug it in and multiply it by the derivative of D. That's how you're left with
So when they say origin, they mean the vertex of the graph? ..or does it even matter where you draw the point at?
Like if in the same problem, y = sin(x) instead of y = x² + 1, would I draw a triangle the same way you did, with the point at (0, 0) instead, and then use the pythagorean theorem? or does it require a different method because it's a trig function?