Double Differentiation

Q. If $y=x^3$, then $\frac{d^{2}y}{d{x}^2}$ is

1. $6x^2$
2. $3x$
3. $6x$
4. $3x^2$

Q. If $y=\sin x$, then $\frac{d^{2}y}{d{x}^2}$ will be

1. $\cos x$
2. $\sin x$
3. $2\sin x$
4. $-\sin x$

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. 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 $y=x^3$, then $\frac{d^{2}y}{d{x}^2}$ is

1. $6x^2$
2. $3x$
3. $6x$
4. $3x^2$

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

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

Q. Find the second derivative of the following function: $y=e^{9x+15}$

1. $81y$
2. $e^{9x+15}$
3. $9e^{9x+15}$
4. $e^{9y}$

Q.

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

1. none of these

2. Maxima :

3. Maxima:

4. Minima:

Q. How do you find the derivative of $Y=\frac{e^x-e^{-x}}{e^x+e^{-x}}$?

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 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 minimum value of a function $y$, represented as $y=x^3-3x^2+6$.

1. $2$
2. $0$
3. $6$
4. $-2$

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. 1

2. 2

3. 2x

4. 

Q.

Find the minimum and maximum value of the function y =x cube - 3x square + 6 find the values of y at which it occurs

Q. If $y=x^3$, then $\frac{d^{2}y}{d{x}^2}$ is

1. $6x^2$
2. $6x$
3. $3x^2$
4. $3x$

Q. Find the minimum value of a function $y$, represented as $y=x^3-3x^2+6$.

1. $2$
2. $0$
3. $6$
4. $-2$

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. Find the minimum value of a function $y$, represented as $y=x^3-3x^2+6$.

1. $2$
2. $0$
3. $6$
4. $-2$

Q. If surface area of a cube is changing at a rate of $6m^2/s$ , find the rate (in $\text{m/s}$) at which length of the body diagonal changes, at a moment when side length is $1m$.

Q.

if f(x)=x cos x, find f"(x), or $\frac{d^{2}y}{d{x}^2}$

1. - xsinx + cosx

2. - xcosx - 2sinx

3. xsinx - cosx

4. none of these

Q. If surface area of a cube is changing at a rate of $6m^2/s$ , find the rate (in $\text{m/s}$) at which length of the body diagonal changes, at a moment when side length is $1m$.

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

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 : 3

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

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

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

Q.

If $\mathrm{f}\left(\mathrm{x}\right)=1+2{\mathrm{x}}^2+2^2{\mathrm{x}}^4+....+2^{10}{\mathrm{x}}^{20}$. Then, f(x) has

1. More than one minimum

2. Exactly one minimum

3. At least one maximum

4. None of the above

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

1. True
2. False

Q.

if f(x)=x cos x, find f"(x), or $\frac{d^{2}y}{d{x}^2}$

1. - xsinx + cosx

2. - xcosx - 2sinx

3. xsinx - cosx

4. none of these

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 derivative of $y=sin(x^2-4)$

1. none of these

2. 

3. 

4. 

Q.

Find the derivative of $y=sin(x^2-4)$

1. $2xcos(x^2-4)$

2. $2xcos{x}^2$

3. $xcos(x^2-4)$

4. none of these