Page:Calculus Made Easy.pdf/114

 readily see that the equation represents a curve with a minimum. These values are plotted in Fig. 26, which shows that $$y$$ has apparently a minimum value of $$3$$, when $$x$$ is made equal to $$2$$. But are you sure that the minimum occurs at $$2$$, and not at $$2\tfrac{1}{4}$$ or at $$1\tfrac{3}{4}$$?

Of course it would be possible with any algebraic expression to work out a lot of values, and in this way arrive gradually at the particular value that may be a maximum or a minimum.



Here is another example:

Let

Calculate a few values thus: