The functional $$\int_{0}^{1}(1+x)(y')^{2}dx,y(0)=0,y(1)=1$$ Possesses
$1.$ Strong maxima.
$2.$ Strong minima.
$3.$ Weak maxima but not a strong maxima.
$4.$ Weak minima but not a strong minima.
I tried it as $F=(1+x)(y')^{2}$ so $F_{y'y'}=2(1+x)>0$ for any $y,y',$ so strong minima by Legendr's conditions. Am i right? Please suggest me. Thanks a lot.