In Mathematica, the maximum of an expression that is a function of one variable can be found with



where expr is a function of x, xo is the initial guess for the search for the minimum or maximum, xl is the lower bound for the search region, and xu is the upper bound for the search region. Both xl and xu are optional.

If you use WolframAlpha online, just type:



Then, move your mouse cursor to the red dot to display the coordinates. And that's for the first graph.



This post has been edited by Critical_Fallacy: Apr 15 2015, 01:52 PM

The linear control mechanism in 2(a) fails to fill up the water level of the tank to 100% because the amount of water it pumps into the tank is insufficient to increase the height of the water level significantly.

It is important to comment on the physical meaning of linear control mechanism, where the flow rate is linearly proportional to measured water level error Δh = (14 - h). As the height of the water level is approaching 14 m, the error signal is greatly reduced Δh ≈ 0, causing the flow rate is throttled to a state where it causes an infinitesimal increase in the water level (e.g. 13.9 m + 0.09 + 0.009 + ...), and it never reach the full tank height.

Technically, this doesn't cause overflow, but is undesirable because the water pump seems to be in perpetual operation (causing the acceleration of wear and tear, and not energy-efficient). Of course, the control system can add a constraint to terminate the pump by installing a simple fail-safe sensor at 13.9 m, if the 0.1 m does not have a significant impact on the commercial side.

The command "FindMaximum[]" returns only the numerical values.

You should plot the numerical evaluation of the equation and then label the result by identifying its maximum value.

(* Find maximum *)



(* Create labels *)



(* Plot and annotate results *)



As you can see, it's pretty systematic and tedious in a sense. A quick shortcut is to use the Tooltip[], which allows you to use a mouse pointer to display information about curves or data points when the mouse pointer is over a curve or a data point.

The use of computational software is probably beyond STPM. The proper way to find the maximum is to solve the following equation:

It's supposed to be very fun! You need the minds of a Mathematician + an Engineer to craft this Magical Box!

How many female students are there in your course?

Because UTHM are mostly engineering courses, it's quite unusual for many girls enrolled in the course.

Then you are lucky!