Double Differentiation

Q. Find the minimum value of the function $y=5x^2-2x+1$.

1. $0.4$
2. $0.8$
3. $1.2$
4. $1.6$

Q.

If $z$ is a complex number such that $\mathrm{Re}\left(z\right)=\mathrm{Im}\left(z\right)$, then

1. $\mathrm{Re}\left(z^2\right)=0$

2. $\mathrm{Im}\left(z^2\right)=0$

3. $\mathrm{Re}\left(z^2\right)=\mathrm{Im}\left(z^2\right)$

4. $\mathrm{Re}\left(z^2\right)=-\mathrm{Im}\left(z^2\right)$

5. $z^2=0$

Q.

If $y=co{s}^{2}x,then\frac{dy}{dx}=?$

1. - sin 2x

2. 2 cos x

3. none of these

4. sin 2x

Q. Find the minimum value of the function $y=5x^2-2x+1$.

1. $0.4$
2. $0.8$
3. $1.2$
4. $1.6$

Q. Double derivative of a quadratic function is a constant.

1. True
2. False

Q.

Find the minimum and maximum value of the function $y=x^3-3x^2+6$. Find the values of y at which it occurs.

1. Maxima at x = 0, Maximum value = 6

2. Maxima at x = 2, Maximum value = 2

3. Minima at x=0, minimum value = 6

4. Minima at x=2, minimum value = 6

Q.

Find the double derivate of y if $y=x^2$

1. 

2. 2x

3. 2

4. 1

Q.

Q.

Find the double derivate of y if $y=x^2$

1. 2

2. 2x

3. 1

4. $x^2$

Q.

Superman is going on a vacation to his home planet krypton from earth via. Sun. (Let's assume for a moment that Krypton is not destroyed). His energy v/s distance travelled graph is as shown below:

Find the number of positions where $\frac{dE}{ds}$=0. Based on this find out the number of stars that Super man crossed on his way home from earth. (I hope you know that superman's source of energy is sunlight or star light so the more closer he goes to a star the more energy he has)

1. number of positions : 3, number of stars : 2

2. number of positions : 2, number of stars : 3

3. number of positions : 3, number of stars : 3

4. number of positions : 2, number of stars : 2

Q. Double derivative of a quadratic function is a constant.

1. True
2. False

Q. The maximum area of a rectangle (in $m^2$) having perimeter $\text{1000 m}$ is

Q. The double derivative at a local maximum is

1. = 0
2. > 0
3. < 0
4. > = 0

Q. Find the second derivative of the following function: $y=e^{3x+2}$

1. $e^{3x+2}$
2. $e^{9y}$
3. $3e^{3x+2}$
4. $9y$

Q. If a function is given as $y=ln\left(sinx\right)$, then $\frac{d^{2}y}{d{x}^2}$ will be

1. $cose{c}^{2}x$
2. $-cose{c}^{2}x$
3. $se{c}^{2}x$
4. $-cose{c}^{2}xcotx$

Q. Find the maximum and minimum values of function $y=2x^3-15x^2+36x+11$

1. $42;41$
2. $39;38$
3. $35;34$
4. $52;51$

Q.

Find the values of x for which A $si{n}^{2}x$ is minimum and Maximum. A is some positive constant.

1. Maxima : $x=N\pi$

2. Maxima: $x=(2N+1)\frac{\pi }{2}$

3. Minima: $x=(2N+1)\pi$

4. none of these