For a,b,cinmathbb R, consider the variational problem: Minimize J[y]=displaystyleint0^2[a,(y')^2+2byy'+cy^2],dx, subject to y(0)=10, y(1)=100. Then which of the following statements are true?

Q99Section C (Part C)99 of 120

Extremals versus minimizers for a quadratic functional with a free end

For $a,b,c\in\mathbb R$ , consider the variational problem:

Minimize $J[y]=\displaystyle\int_0^2\big[a\,(y')^2+2byy'+cy^2\big]\,dx$ , subject to $y(0)=10$ , $y(1)=100$ .

Then which of the following statements are true?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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