Point of Inflection

Q.

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

1. 0

2. 1

3. 2

4. -1

Q.

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

1. f(x) = sin(x)

2. f(x) = cos (x)

3. f(x) = x²

4. f(x) = x³

Q.

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

1. False

2. True

Q. The function $y=\frac{\mathrm{ax}+b}{\left(x-1\right)\left(x-4\right)}$ has a turning point or a point of inflexion at P(2, -1). Then, which of the following is(are) true about a and b?

1. a = 0
2. a = 1
3. b = 1
4. b = 0

Q. Which of the following is (are) true about the function $f\left(x\right)=4x^3–18x^2+27x–7$ ?

1. Has a maxima at x = 3/2
2. x = 3/2 is a point of inflexion
3. Has a minima at x = 3/2
4. Neither has a maxima nor minima

Q. Which of the following function(s) has/have point of inflection?

1. $f\left(x\right)=x^{6/7}$
2. $f\left(x\right)=x^6$
3. $f\left(x\right)=\cos x+2x$
4. $f\left(x\right)=x|x|$

Q. Let $f\left(x\right)$ be a twice differentiable function and has no critical points. Let $g\left(x\right)=(x+6{)}^{2009}(x+1{)}^{2010}(x+2{)}^{2011}(x-3{)}^{2012}(x-4{)}^{2013}(x-5{)}^{2014}$ be such that $f\left(x\right)+g\left(x\right)f^{\prime }\left(x\right)+f^{\prime \prime }\left(x\right)=0.$ Then the function $h\left(x\right)=f^2\left(x\right)+(f^{\prime }\left(x\right){)}^2$

1. is monotonically increasing in $(-2,4)$.
2. has exactly three points of inflection.
3. has exactly two points of local maxima.
4. has a negative point of local minimum.

Q. The graph of $f\left(x\right)=\frac{x^5}{20}-\frac{x^4}{12}+5$ has

1. one local maximum and one local minimum
2. one local minimum and one point of inflection.
3. one local maximum, one local minimum and one point of inflection.
4. one local maximum, one local minimum and two points of inflection.

Q. Match the column

Q. The condition for $y=a{x}^4+b{x}^3+c{x}^2+dx+e$ to have points of inflection is

1. $b^2-4ac>0$
2. $3b^2-8ac=0$
3. $3b^2-8ac>0$
4. $3b^2-8ac<0$