85729 For real number \(x\), if the minimum value of \(f(x)\) \(=x^{2}+2 b x+2 c^{2}\) is greater than the maximum value of \(g(x)=-x^{2}-2 c x+b^{2}\), then

85730 The sum of the maximum and the minimum values of \(3 x^{4}-2 x^{3}-6 x^{2}+6 x+4\), in \((0,2)\) is

85731 If \(p\) and \(q\) are respectively the global maximum and global minimum of the function \(f(x)=x^{2} e^{2 x}\) on the interval \([-2,2]\),
then \(\mathrm{pe}^{-4}+\mathrm{qe}^{4}=\)

85732 From a rectangular sheet having dimensions 30 \(\mathbf{c m} \times 80 \mathrm{~cm}\), four equal squares of side \(x \mathrm{~cm}\) are cut at each corner. The remaining sides of the rectangle are folded up vertically so as to form an open rectangular box. Find the value of ' \(x\) ' for which the volume of the box formed is maximum.

85729 For real number \(x\), if the minimum value of \(f(x)\) \(=x^{2}+2 b x+2 c^{2}\) is greater than the maximum value of \(g(x)=-x^{2}-2 c x+b^{2}\), then

85730 The sum of the maximum and the minimum values of \(3 x^{4}-2 x^{3}-6 x^{2}+6 x+4\), in \((0,2)\) is

85731 If \(p\) and \(q\) are respectively the global maximum and global minimum of the function \(f(x)=x^{2} e^{2 x}\) on the interval \([-2,2]\),
then \(\mathrm{pe}^{-4}+\mathrm{qe}^{4}=\)

85732 From a rectangular sheet having dimensions 30 \(\mathbf{c m} \times 80 \mathrm{~cm}\), four equal squares of side \(x \mathrm{~cm}\) are cut at each corner. The remaining sides of the rectangle are folded up vertically so as to form an open rectangular box. Find the value of ' \(x\) ' for which the volume of the box formed is maximum.

85729 For real number \(x\), if the minimum value of \(f(x)\) \(=x^{2}+2 b x+2 c^{2}\) is greater than the maximum value of \(g(x)=-x^{2}-2 c x+b^{2}\), then

85730 The sum of the maximum and the minimum values of \(3 x^{4}-2 x^{3}-6 x^{2}+6 x+4\), in \((0,2)\) is

85731 If \(p\) and \(q\) are respectively the global maximum and global minimum of the function \(f(x)=x^{2} e^{2 x}\) on the interval \([-2,2]\),
then \(\mathrm{pe}^{-4}+\mathrm{qe}^{4}=\)

85732 From a rectangular sheet having dimensions 30 \(\mathbf{c m} \times 80 \mathrm{~cm}\), four equal squares of side \(x \mathrm{~cm}\) are cut at each corner. The remaining sides of the rectangle are folded up vertically so as to form an open rectangular box. Find the value of ' \(x\) ' for which the volume of the box formed is maximum.

85729 For real number \(x\), if the minimum value of \(f(x)\) \(=x^{2}+2 b x+2 c^{2}\) is greater than the maximum value of \(g(x)=-x^{2}-2 c x+b^{2}\), then

85730 The sum of the maximum and the minimum values of \(3 x^{4}-2 x^{3}-6 x^{2}+6 x+4\), in \((0,2)\) is

85731 If \(p\) and \(q\) are respectively the global maximum and global minimum of the function \(f(x)=x^{2} e^{2 x}\) on the interval \([-2,2]\),
then \(\mathrm{pe}^{-4}+\mathrm{qe}^{4}=\)

85732 From a rectangular sheet having dimensions 30 \(\mathbf{c m} \times 80 \mathrm{~cm}\), four equal squares of side \(x \mathrm{~cm}\) are cut at each corner. The remaining sides of the rectangle are folded up vertically so as to form an open rectangular box. Find the value of ' \(x\) ' for which the volume of the box formed is maximum.