Tweet
Re: Official Bored at Work / Off-Topic Chat Thread II
Well, just to do a sanity check, an x^2 - 1 function is going to look like a U centered around the y-axis. The point has a positive x value, so it's on the right side of the U, and its decreasing, so moving towards the center. Following the curve, we can see that y is decreasing moving in that direction, so whatever value we get will be negative. And knowing something about the square function, for values x>1, the graph moves much more vertically than horizontally, so whatever value we get for the y movement will be greater than what we have for the x.
What I did was take the derivative of the function so I could find the slope of the line at (2,3). Derivative of x^2 is 2x, plugging in the x value of our point tells us that the slope of the tangent there is 2(2) = 4. Slope equals delta y over delta x, so delta y equals slope times delta x, which is 4(-2), so -8.
I don't know how to properly notate that as a progression of equations, and I'm mixing algebra terms and calculus ones, but I believe that that is correct.
Well, just to do a sanity check, an x^2 - 1 function is going to look like a U centered around the y-axis. The point has a positive x value, so it's on the right side of the U, and its decreasing, so moving towards the center. Following the curve, we can see that y is decreasing moving in that direction, so whatever value we get will be negative. And knowing something about the square function, for values x>1, the graph moves much more vertically than horizontally, so whatever value we get for the y movement will be greater than what we have for the x.
What I did was take the derivative of the function so I could find the slope of the line at (2,3). Derivative of x^2 is 2x, plugging in the x value of our point tells us that the slope of the tangent there is 2(2) = 4. Slope equals delta y over delta x, so delta y equals slope times delta x, which is 4(-2), so -8.
I don't know how to properly notate that as a progression of equations, and I'm mixing algebra terms and calculus ones, but I believe that that is correct.
Comment