Function in Maple giving weird plots

Question

In Maple I have defined a function

If I plot within $Q \in [0,100]$ I get

but I get the exact same plot with other boundaries

and if I use $Q \in [0, 10^{-10}]$ I get

How can this happen? What am I doing wrong? I think the last plot is edged because the steps on the y axis is so small that it cannot draw the line as curved as it should be. But I have no idea why the same function can draw the same linear curve ending in different values of $Q$.

Answer 1

The quadratic term is much smaller than the linear term. The closer you look at any curve, by narrowing the range of $x$, the straighter it will look. Instead, try larger ranges of $x$, you will start to see the curve.
For the very narrow range, Maple doesn't store numbers between 44.99999999999997 and 44.99999999999998. This is called round-off error. It happens so rarely that we need the seventeenth decimal place. Also it takes space to store, and time to calculate. I think you can ask Maple to change that precision.

Answer 2

Nothing wrong with the Maple output. The coefficients you provide for the quadratic are miniscule, so for practical purposes, on your indicated range, the function is very close to:

$$PN(Q)=-3.3\cdot 10^{-4}Q+45$$

which is a line of very small slope. To see the quadratic nature of the original, versus the linear approximation, try increasing the desired range:

P := proc (Q) options operator, arrow; 7.4*(1/10000000000)*Q^2+(-1)*3.3*(1/10000)*Q+45 end proc;
PN := proc (Q) options operator, arrow; (-1)*3.3*(1/10000)*Q+45 end proc;

and then:

plot({P(Q), PN(Q)}, Q = -10^6 .. 10^6, color = [red, green]);