Page:Calculus Made Easy.pdf/126

 (3) Find the maxima and minima of the function

We get

for maximum or minimum; or

There is only one value, hence only one maximum or minimum.

it is therefore a minimum. (It is instructive to plot the graph of the function.)

(4) Find the maxima and minima of the function $$y=\sqrt{1+x}+\sqrt{1-x}$$. (It will be found instructive to plot the graph.)

Differentiating gives at once (see example No. 1, p.68)

for maximum or minimum.

Hence $$\sqrt{1+x}=\sqrt{1-x}$$ and $$x=0$$, the only solution

For $$x=0$$, $$y=0$$.

For $$x=\pm 5$$, $$y=1.932$$, so this is a maximum.