Luke: derivatives, max and mins, and critical points

My name is Luke. ┬áSo far of all the classes I’ve taken one of my favorite is calculus. One of the parts that I found interesting was when we looked at graphs of functions and matched them with graphs of their derivatives. For example finding the local max and mins of the graphs and then seeing that these values are where the derivative of that function equals zero.

Here is a link that uses the derivatives to graph the original function but the idea is same.

Here is a link that explains what max and mins are and how they are related to critical points of functions which can be found using differentiation.

An example of a derivative would be:

$x^3+x^2+4$

$\frac{d}{dx} (x^3+x^2+4)=3x^2+2x$

 

2 thoughts on “Luke: derivatives, max and mins, and critical points

  1. farrghunabdulrahim

    Studying derivatives is interesting topic in its own right. But from what I have seen in the past, students who first start studying derivatives in first course of Calculus don’t even understand the meaning of minimum and maximum work from Geometric perspective. For me personally, the geometric properties of finding the minimum, maximum, and critical points is more interesting that solving for $3x^2+2x=0$. What are your thoughts on that?

  2. Janae Korfanta

    I also find matching graphs with the graph of their derivatives interesting. Especially if the function being examined is a position function for an object. If this is the case, I also like to get into the third derivative and find it cool that by manipulating one function you can learn an object’s position, speed, and acceleration simply by taking derivatives.

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