G Tewani Solutions for Chapter: Monotonicity and Maxima-Minima of Functions, Exercise 4: DPP

If $a, b\in R$ distinct numbers satisfying $\left|a-1\right|+\left|b-1\right|=\left|a\right|+\left|b\right|=\left|a+1\right|+\left|b+1\right|,$ then the minimum value of $\left|a-b\right|$ is:

If the equation $2x^3-6x+2\sin a+3=0$, where $a\in (0$$,$$\pi )$ has only one real root, then the largest interval in which $a$ lies is:

Let $f$ be a continuous and differentiable function in $\left(x_1, x_2\right)$. If $f\left(x\right).f^{\text{'}}\left(x\right)\ge x\sqrt{1-{\left(f\left(x\right)\right)}^4}$, $\underset{x\to x_1^{+}}{\lim }{\left(f\left(x\right)\right)}^2=1$ and $\underset{x\to x_2-}{\lim }{\left(f\left(x\right)\right)}^2=\frac{1}{2}$, then the minimum value of $\left(x_1^2-x_2^2\right)$ is:

If $ab=2a+3b$, $a>0$, $b>0$, then the minimum value of $ab$ is:

Let $a, b, c, d, e, f, g$ and $h$, be distinct elements in the set $\left\{-7, -5, -3, -2, 2, 4, 6, 13\right\}$. Then, the minimum value of $(a+b+c+d{)}^2+(e+f+g+h{)}^2$ is:

The perimeter of a sector of a circle is $p.$ The area of the sector is maximum when its radius is:

Minimum integral value of $k$ for which the equation $e^x=k{x}^2$ has exactly three real distinct solutions is:

Let $f\left(x\right)=x^3-3x+1.$ Then number of different real solutions of $f\left(f\left(x\right)\right)=0$