I'm attempting to analytically stitch together two linear functions with two quadratic functions. The function I'm considering, then, is a piecewise function consisting of 4 parts. Below are the values I'm considering for the scenario as well as the function itself. 

k1 = 1.41; k2 = 1.45; eps1 = 2*^8; eps2 = 3.5*^8; p0 = 1.04*^8; delP = 0.01*^8;
kmax = (1/2)(k1 + k2) + (k2 p0 + eps2 - k1 p0 - eps1)/delP;
edens[p_] := Piecewise[{{k1 p + eps1, p &lt;= p0 - delP},
                    {(1/2)(kmax - k1)/delP * (p-p0)^2 + kmax(p-p0) + (k1 p0 + eps1) + (1/2)delP * (kmax - k1), p0-delP &lt;= p &lt;= p0},
                    {(1/2)(k2 - kmax)/delP * (p-p0)^2 + kmax(p-p0) + (k2 p0 + eps2) + (1/2)delP * (k2 - kmax), p0 &lt;= p &lt;= p0+delP},
                    {k2 p + eps2, p &gt;= p0 + delP}}];


This function is continuous and differentiable at the boundary points, which you can see by plotting it:

Plot[edens[p], {p, p0 - 2*delP, p0 + 2*delP}, Exclusions -&gt; None]




However, if I try and evaluate the derivative of this function at the boundary points (p0, p0-delP, and p0+delP), I get Indeterminate even though the value is the same on both sides.

I have a feeling this is because I'm using approximate real numbers. Is there anyway to force Mathematica to say that the derivative at a boundary point is a specific value?


Question: How to highlight part of an image and blur the rest?
Answer: I made a JSfiddle to demonstrate how a blur effect can be achieved. Ideally what you want to do is have it where, when you hover over the image, the rest of the page uses the blur effect. The rest of the page can be separated using a 

So, using my code, what you want is something like:

&lt;div class=blur&gt;
Code of other stuff
&lt;/div&gt;
&lt;img href="example.jpg"&gt;
&lt;div class=blur&gt;
More code...
&lt;/div&gt;


To make the photo stick out, give the photo a high z-index then have a position:fixed div that has a z-index lower than the selected item. 

Here's some more code  that I found that demonstrates how to do this blur effect, a bit more complex than mine though. 

If you have any more questions, feel free to ask.