Page:Calculus Made Easy.pdf/116

 Differentiating, we get:

Now equate this to zero, thus:

Solving this equation for $$x$$, we get:

Now, we know that the maximum (or minimum) will occur exactly when $$x=2$$.

Putting the value $$x=2$$ into the original equation, we get

Now look back at Fig 26, and you will see that the minimum occurs when $$x=2$$, and that this minimum of $$y=3$$.

Try the second example (Fig. 24), which is

Differentiating,

Equating to zero,

whence

and putting this value of $$x$$ into the original equation, we find:

This gives us exactly the information as to which the method of trying a lot of values left us uncertain.