Maxima and Minima
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Application of Derivatives

85624 The curve \(y=x e^{x}\) has minimum value equal to

1 \(-\frac{1}{\mathrm{e}}\)
2 \(\frac{1}{\mathrm{e}}\)
3 \(-\mathrm{e}\)
4 e
BITSAT-2016
Application of Derivatives

85625 A cylindrical gas container is closed at the top and open at the bottom. if the iron plate of the top is \(\frac{5}{4}\) time as thick as the plate forming the cylindrical sides. The ratio of the radius to the height of the cylinder using minimum material for the same capacity \(i\)

1 \(\frac{2}{3}\)
2 \(\frac{1}{2}\)
3 \(\frac{4}{5}\)
4 \(\frac{1}{3}\)
BITSAT-2017
Application of Derivatives

85626 If \(f(x)=\sin x+2 \cos ^{2} x, \frac{\pi}{4} \leq x \leq \frac{3 \pi}{4}\) Then, \(f\) attains its

1 minimum at \(\mathrm{x}=\frac{\pi}{4}\)
2 maximum at \(\mathrm{x}=\frac{\pi}{2}\)
3 minimum at \(\mathrm{x}=\frac{\pi}{2}\)
4 maximum at \(x=\sin ^{-1}\left(\frac{1}{4}\right)\)
WB JEE-2013
Application of Derivatives

85627 The maximum and minimum values of \(\cos ^{6} \theta+\sin ^{6} \theta\) are respectively

1 1 and \(\frac{1}{4}\)
2 1 and 0
3 2 and 0
4 1 and \(\frac{1}{2}\)
WB JEE-2013
NEET DIGITAL LIBRARY
Application of Derivatives

85624 The curve \(y=x e^{x}\) has minimum value equal to

1 \(-\frac{1}{\mathrm{e}}\)
2 \(\frac{1}{\mathrm{e}}\)
3 \(-\mathrm{e}\)
4 e
BITSAT-2016
Application of Derivatives

85625 A cylindrical gas container is closed at the top and open at the bottom. if the iron plate of the top is \(\frac{5}{4}\) time as thick as the plate forming the cylindrical sides. The ratio of the radius to the height of the cylinder using minimum material for the same capacity \(i\)

1 \(\frac{2}{3}\)
2 \(\frac{1}{2}\)
3 \(\frac{4}{5}\)
4 \(\frac{1}{3}\)
BITSAT-2017
Application of Derivatives

85626 If \(f(x)=\sin x+2 \cos ^{2} x, \frac{\pi}{4} \leq x \leq \frac{3 \pi}{4}\) Then, \(f\) attains its

1 minimum at \(\mathrm{x}=\frac{\pi}{4}\)
2 maximum at \(\mathrm{x}=\frac{\pi}{2}\)
3 minimum at \(\mathrm{x}=\frac{\pi}{2}\)
4 maximum at \(x=\sin ^{-1}\left(\frac{1}{4}\right)\)
WB JEE-2013
Application of Derivatives

85627 The maximum and minimum values of \(\cos ^{6} \theta+\sin ^{6} \theta\) are respectively

1 1 and \(\frac{1}{4}\)
2 1 and 0
3 2 and 0
4 1 and \(\frac{1}{2}\)
WB JEE-2013
Join With Us for More Updates
Application of Derivatives

85624 The curve \(y=x e^{x}\) has minimum value equal to

1 \(-\frac{1}{\mathrm{e}}\)
2 \(\frac{1}{\mathrm{e}}\)
3 \(-\mathrm{e}\)
4 e
BITSAT-2016
Application of Derivatives

85625 A cylindrical gas container is closed at the top and open at the bottom. if the iron plate of the top is \(\frac{5}{4}\) time as thick as the plate forming the cylindrical sides. The ratio of the radius to the height of the cylinder using minimum material for the same capacity \(i\)

1 \(\frac{2}{3}\)
2 \(\frac{1}{2}\)
3 \(\frac{4}{5}\)
4 \(\frac{1}{3}\)
BITSAT-2017
Application of Derivatives

85626 If \(f(x)=\sin x+2 \cos ^{2} x, \frac{\pi}{4} \leq x \leq \frac{3 \pi}{4}\) Then, \(f\) attains its

1 minimum at \(\mathrm{x}=\frac{\pi}{4}\)
2 maximum at \(\mathrm{x}=\frac{\pi}{2}\)
3 minimum at \(\mathrm{x}=\frac{\pi}{2}\)
4 maximum at \(x=\sin ^{-1}\left(\frac{1}{4}\right)\)
WB JEE-2013
Application of Derivatives

85627 The maximum and minimum values of \(\cos ^{6} \theta+\sin ^{6} \theta\) are respectively

1 1 and \(\frac{1}{4}\)
2 1 and 0
3 2 and 0
4 1 and \(\frac{1}{2}\)
WB JEE-2013
For More Updates join with Us
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Application of Derivatives

85624 The curve \(y=x e^{x}\) has minimum value equal to

1 \(-\frac{1}{\mathrm{e}}\)
2 \(\frac{1}{\mathrm{e}}\)
3 \(-\mathrm{e}\)
4 e
BITSAT-2016
Application of Derivatives

85625 A cylindrical gas container is closed at the top and open at the bottom. if the iron plate of the top is \(\frac{5}{4}\) time as thick as the plate forming the cylindrical sides. The ratio of the radius to the height of the cylinder using minimum material for the same capacity \(i\)

1 \(\frac{2}{3}\)
2 \(\frac{1}{2}\)
3 \(\frac{4}{5}\)
4 \(\frac{1}{3}\)
BITSAT-2017
Application of Derivatives

85626 If \(f(x)=\sin x+2 \cos ^{2} x, \frac{\pi}{4} \leq x \leq \frac{3 \pi}{4}\) Then, \(f\) attains its

1 minimum at \(\mathrm{x}=\frac{\pi}{4}\)
2 maximum at \(\mathrm{x}=\frac{\pi}{2}\)
3 minimum at \(\mathrm{x}=\frac{\pi}{2}\)
4 maximum at \(x=\sin ^{-1}\left(\frac{1}{4}\right)\)
WB JEE-2013
Application of Derivatives

85627 The maximum and minimum values of \(\cos ^{6} \theta+\sin ^{6} \theta\) are respectively

1 1 and \(\frac{1}{4}\)
2 1 and 0
3 2 and 0
4 1 and \(\frac{1}{2}\)
WB JEE-2013
NEET DIGITAL LIBRARY