1. ## Significance of Derivative?

Hi,

I calculated the derivative of this parabola:

Parabola: $\displaystyle y = \frac{1}{4} x^2$

Derivative: $\displaystyle \frac{dy}{dx} = \frac{1}{2} x$

So what exactly does this derivative mean? I'm going from one function to another, but what can I possibly deduce from the second function?

Thanks.

2. ## Re: Significance of Derivative?

The derivative tells you the slope of your function at any point x.

3. ## Re: Significance of Derivative?

If you have a straight line, the slope is equal in each point of the straight line. But if you have a curve the slope isn't equal in each point of the curve and so with derivatives you can determine the slope of the curve at any point. The reason for example if you calculate the first derivative to see where a given function increases/decreases (so you take $\displaystyle f'(x)=0$) is that when the slope is 0 that means the tangent line is parallel to the x-axis and this is only possible if you've a minimum or a maximum of the curve.

4. ## Re: Significance of Derivative?

I understand now, thanks!