List of top Mathematics Questions on Maxima and Minima asked in MHT CET

A wire 64 m long is bent into the shape of a rectangle. What should be its dimensions so that the enclosed area is maximum?

A manufacturer sells $x$ items at a price of ₹$(6 - \frac{x}{40})$ each. The cost price of $x$ items is ₹$(\frac{x}{5} + 193)$. The maximum profit in ₹ is ______.

The maximum value of $xy$ when $x+2y=8$ is

The function $f(x) = x^3 - 6x^2 + 9x + 2$ has maximum value when $x$ is

A rectangle of maximum area is inscribed in an ellipse $\frac{x^2}{25} + \frac{y^2}{16} = 1$, then its dimensions are

If $f(x) = x^2 + ax + b$ has minima at $x = 3$ whose value is $5$, then the values of $a$ and $b$ are respectively

10 is divided into two parts such that the sum of double of the first and square of the other is minimum, then the numbers are respectively

If $x = -2$ and $x = 4$ are the extreme points of the function $y = x^3 - \alpha x^2 - \beta x + 5$, then the values of $\alpha$ and $\beta$ are respectively

For all real $x$, the minimum value of the function $f(x) = \frac{1 - x + x^2}{1 + x + x^2}$ is

The maximum area of the rectangle that can be inscribed in a circle of radius $r$ is

For all real $x$, the minimum value of the function $f(x) = \frac{1 - x + x^2}{1 + x + x^2}$ is

A wire of length 20 units is divided into two parts such that the product of one part and cube of the other part is maximum, then product of these parts is

The maximum value of the function $f(x) = 3x^3 - 18x^2 + 27x - 40$ on the set $S = \{x \in \mathbb{R} \mid x^2 + 30 \le 11x\}$ is