Point of Inflection

Q. The number of integral value(s) of $a$ for which $f\left(x\right)=\{\begin{array}{cc}{a}^2-3+\sin x,& 0<x<\frac{\pi }{2}\\ 1+\cos x,& \frac{\pi }{2}\le x<\pi \end{array}$ has a point of local maxima at $x=\frac{\pi }{2},$ is

Q. The number of critical point(s) for $f\left(x\right)=\frac{5}{4}(x-1{)}^{\frac{4}{5}}+x,$ is

1. More than $2$
2. $1$
3. $0$
4. $2$

Q. The total number of extremum point(s) for $f\left(x\right)=x^3+x^2+x+1$ is

Q.

Which of the following function has a point of inflection at x = 0 ?

1. $f\left(x\right)=sin\left(x\right)$

2. $f\left(x\right)=cos\left(x\right)$

3. $f\left(x\right)=x^2$

4. $f\left(x\right)=x^3$

Q.

Point of inflection of the function $f\left(x\right)=x^3$ is

1. 0

2. 1

3. 2

4. -1

Q.

Point of inflection is the point in the domain where function changes from convex to concave.

1. True

2. False

Q.

Point of inflection is the point in the domain where function changes from convex to concave.

1. True

2. False

Q. $f\left(x\right)=(x-1)(x-2)(x-3)$ has a local minima when $x$ is equal to

1. $2+\frac{1}{\sqrt{3}}$
2. $2-\frac{1}{\sqrt{3}}$
3. $3-\frac{1}{\sqrt{2}}$
4. $3+\frac{1}{\sqrt{2}}$