nth Derivative Test

Q. The set of points, where $f\left(x\right)=\frac{x}{1+|x|}$ is differentiable, is

1. $(-\infty ,\infty )$
2. $(-\infty ,-1)\cup (-1,\infty )$
3. $(0,\infty )$
4. $(-\infty ,0)\cup (0,\infty )$

Q. If $f\left(x^5\right)=5x^3$, then $f^{\prime }\left(x\right)=$

1. $\frac{3}{\sqrt[5]{5x^2}}$
2. $\frac{3}{\sqrt[5]{5x}}$
3. $\sqrt[5]{5x}$
4. $\frac{3}{x}$

Q.

At which of the following points does $f\left(x\right)=x^4$ has a maximum?

1. 0

2. 1

3. 2

4. None of these

5. 3

Q.

$f\left(x\right)=6x^5$ has a maximum at x = 0.

1. True

2. False

Q.

$f\left(x\right)=6x^5$ has a maximum at x = 0.

1. True

2. False

Q.

At which of the following points does $f\left(x\right)=x^4$ has a maximum?

1. 0

2. 1

3. 2

4. 3

5. None of these

Q. Let$x_n={(1-\frac{1}{3})}^2{(1-\frac{1}{6})}^2{(1-\frac{1}{10})}^2....{(1-\frac{1}{\frac{n(n+1)}{2}})}^2,n\ge 2.$
Then the value of $\underset{n\to \infty }{lim}{x}_n$ is

1. $\frac{1}{3}$
2. $\frac{1}{9}$
3. $\frac{1}{81}$
4. $0$ (zero)

Q.

At which of the following points does $f\left(x\right)=x^4$ has a maximum?

1. 0

2. 1

3. 2

4. 3

5. None of these

Q.

$f\left(x\right)=6x^5$ has a maximum at x = 0.

1. True

2. False

Q. If $xy(y-x)=2a^3$, at what point does y have a minimum value .

1. a, -a
2. None of these
3. 2a, 2a
4. a, 2a

Q. Find the interval of monotonocity of the function $f\left(x\right)=\frac{\left|x-1\right|}{x^2}.$