Derivatives of Curves. How do they work? How is the second derivative of a quadratic equation a constant? Is the second derivative the slope of the slope?
In: Mathematics
>Is the second derivative the slope of the slope?
That’s exactly right.
>How is the second derivative of a quadratic equation a constant?
It just is. That’s more or less how a quadratic is defined, its a shape whose second derivative is constant, a shape whose slope increases proportionally to the x or whatever input you are using.
The derivative definition of the limit as h approaches x of (f(x) – f(h))/(x – h) is pretty self explanatory imo. This is just the slope formula, rise over run, but taken to an infinitesimally small rise over an infinitesimally small run.
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