A box is made with square base and open top. The area of the material used is 192 sq. cms. If the volume of the box is maximum, the dimensions of the box are
area of box
$$192=a^2+4ha$$
volume of box $$=a^2 h$$
$$=a^2\dfrac {(192-a^2)}{4a}$$
$$=a(192-a^2)$$
$$\dfrac {dv}{da}=(192-a^2)-2a^2$$
$$a^2=64$$
$$a=8$$ $$h=4$$
Let $$f,\ g$$ and $$h$$ be real-valued functions defined on the interval $$[0,1]$$ by $$f(x)=e^{x^{2}}+e^{-x^{2}},\ g(x) =xe^{x^{2}}+e^{-x^{2}}$$ and $$h(x)=x^{2}e^{x^{2}}+e^{-x^{2}}$$ If $$a,\ b$$ and $$c$$ denote, respectively, the absolute maximum of $$f,\ g$$ and $$h$$ on $$[0,1]$$ respectively then
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