List of top Mathematics Questions on Maxima and Minima asked in JEE Main

Let the maximum and minimum values of \[\left( \sqrt{8x - x^2 - 12 - 4} \right)^2 + (x - 7)^2, \quad x \in \mathbb{R} \text{ be } M \text{ and } m \text{ respectively}.\] Then $ M^2 - m^2 $ is equal to _____.

Let $ f(x) = 3\sqrt{x - 2} + \sqrt{4 - x} $ be a real-valued function. If $ \alpha $ and $ \beta $ are respectively the minimum and the maximum values of $ f $, then $ \alpha^2 + 2\beta^2 $ is equal to:

The number of critical points of the function $f(x) = (x - 2)^{2/3}(2x + 1)$ is:

Let $f(x) = 4\cos^3 x + 3\sqrt{3} \cos^2 x - 10$. The number of points of local maxima of $f$ in interval $(0, 2\pi)$ is:

Let the set of all positive values of $ \lambda $, for which the point of local minimum of the function $(1 + x (\lambda^2 - x^2)) \frac{x^2 + x + 2}{x^2 + 5x + 6} < 0$ be $(\alpha, \beta)$.
Then $ \alpha^2 + \beta^2 $ is equal to ________.

If the function $f(x) = 2x^3 - 9ax^2 + 12a^2x + 1, \, a>0$ has a local maximum at $x = \alpha$ and a local minimum at $x = \alpha^2$, then $\alpha$ and $\alpha^2$ are the roots of the equation:

The absolute minimum value, of the function $f(x)=\left|x^2-x+1\right|+\left[x^2-x+1\right]$, where $[t]$ denotes the greatest integer function, in the interval $[-1,2]$, is:

A wire of length $20 m$ is to be cut into two pieces A piece of length $l_1$ is bent to make a square of area $A_1$ and the other piece of length $l_2$ is made into a circle of area $A_2$ If $2 A_1+3 A_2$ is minimum then $\left(\pi l_1\right): l_2$ is equal to:

Let $f, g$ and $h$ be the real valued functions defined on $R$ as $f(x)=\begin{cases} \frac{x}{|x|}, & x \neq 0 \\1, & x=0\end{cases}, g(x)=\begin{cases} \frac{\sin (x+1)}{(x+1)}, & x \neq-1 \\1, & x=-1\end{cases}$ and $h(x)=2[x]-f(x)$, where $[x]$ is the greatest integer $\leq x$ Then the value of $\displaystyle\lim _{x \rightarrow 1} g(h(x-1))$ is

The remainder when $(2023)^{2023}$ is divided by $35$ is _____

The sum of the absolute maximum and minimum values of the function $f(x)=\left|x^2-5 x+6\right|-3 x+2$ in the interval $[-1,3]$ is equal to :

The sum of the maximum and minimum values of the function |5x-7|+[x²+2x] is the interval $\left[\frac{5}{4}, 2\right]$, where $[t]$ is the greatest integer $\leq t$ is ______

Let the function $f(x)=2 x^3+(2 p-7) x^2+3(2 p-9) x-6$ have a maxima for some value of $x<0$ and a minima for some value of $x>0$ Then, the set of all values of $p$ is

Let $M$ be the maximum value of the product of two positive integers when their sum is 66. Let the sample space $S =\left\{x \in Z : x(66-x) \geq \frac{5}{9} M\right\}$ and the event $A =\{x \in S : x$ is a multiple of 3$\}$. Then $P ( A )$ is equal to

Let $M$ be the maximum value of the product of two positive integers when their sum is 66 Let the sample space $S =\left\{x \in Z : x(66-x) \geq \frac{5}{9} M\right\}$ and the event $A =\{x \in S : x$ is a multiple of 3$\}$ Then $P ( A )$ is equal to

Let a, b, c and d be positive real numbers such that a + b + c + d = 11. If the maximum value of $a^5b ^3c ^2d$ is $3750\;\beta$, then the value of $\beta$ is

f the maximum value of a, for which the function
$fa(x)=\tan^{−1}\ ⁡2x−3ax+7$
is non-decreasing in $(−\frac{π}{6},\frac{π}{6})$, is a―, then $f\overline{a}(\frac{π}{8}) $
is equal to