can tell from the mathematical expression that this is probably a parabola, it's a quadratic and so if we just create a set of scalar values that we can feed in using for example a range from negative 5 to 5 in steps of 0.25. So this is so x is just from negative 5 to 5 not including 5 in steps of 0.25 and we can actually call this function on this numpy array as well so we get a set of y's if we call f on x's and these y's are basically also applying the function on every one of these elements independently and we can plot this using matplotlib. So plt.plot x's and y's and we get a nice parabola. So previously here we fed in 3.0 somewhere here and we received 20 back which is here the y-coordinate. So now I'd like to think through what is the derivative of this function at any single input point x. So what is the derivative at different points x of this function? Now if you remember back to your calculus class you've probably derived derivatives so we take this mathematical expression 3x squared minus 4x plus 5 and you would write out on a piece of paper and you would apply the product rule and all the other rules and derive the mathematical expression of the great derivative of the original function and then you could plug in different texts and see what the derivative is. We're not going to actually do that because no one in neural networks actually writes out the expression for the neural net. It would be a massive expression, it would be thousands, tens of thousands of terms. No one actually derives the derivative of course and so we're not going to take this kind of like symbolic approach. Instead what I'd like to do is I'd like to look at the definition of derivative and just make sure that we really understand what the derivative is measuring, what it's telling you about the function. And so if
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