Point of Inflection

Q.

Complete set of values of 'a' such that $\frac{x^2-x}{1-ax}$ attains all real values is :

1. [1, 4]

2. [0, 4]

3. [1, ∞]

4. [0, 1]

Q. If the line x-y+2=0 is a normal to the parabola y^2-6y-4x+k=0 . find

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. 38. the coordinaces of a point on the parabola y2=4x which is closest tn the circtc x2+y2-6y+8 =0, are 1. (1, 2) 2. (2, 1) 3. (0, 0) 4. (3/2, 3/2)

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. $0$
3. $1$
4. $2$

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

Q. how many variables does yx^2+3x-c=0 has?

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

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