nth Derivative Test

Q.

Local maximum and local minimum values of the function $\left(x-1\right){\left(x+2\right)}^2$ are

1. $-4,0$

2. $0,-4$

3. $4,0$

4. None of these

Q.

The area bounded by the curves $y=-\sqrt{-x},x=-\sqrt{-y}$ where $x,y\le 0,$ is

1. $\frac{1}{3}$

2. $\frac{1}{4}$

3. $\frac{1}{5}$

4. $\frac{1}{2}$

Q.

The area (in sq units) of the plane region bounded by the curve $x=y^2-2$ and the line $y=-x$ is

1. $\frac{13}{3}$

2. $\frac{2}{5}$

3. $\frac{9}{2}$

4. $\frac{5}{2}$

5. $\frac{13}{2}$

Q.

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

1. True

2. False

Q. If $(1,3)$ is the point of inflection of the curve $y=a{x}^3+b{x}^2,$ then the value of $4(a^2+b^2)$ is

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