List of top Mathematics Questions on Maxima and Minima

The absolute maximum and minimum values of the function \[ f(x)=\sin x+\sqrt3\cos x,\quad x\in[0,\pi] \] are:

If $f(x)=2x^{3}-3x^{2}-\lambda x+1, x\in[0,3]$ attains a local minimum at $x=2$, then the value of $\lambda$ is equal to

The minimum of $f(x) = \dfrac{x^{100} - 1}{x^{100} + 1}, \; x \in \mathbb{R}$ is:

The value of x is maximum for

If \( x+y=50 \), then the maximum value of \( \sqrt{4xy} \) is

If the function $f(x)=ax^3-9x^2+6ax+6$ attains maximum at $x=1$ and minimum at $x=2$, then the value of $a$ is:

If $a+b=10$ and $ab$ is maximum, then the value of a is

Let $f(x)=10-|x-3|,\; x\in\mathbb{R}$. The maximum of $f(x)$ occurs at:

Let \( f(x) = x^2 + ax + \beta \). If \( f \) has a local minimum at \( (2,6) \), then \( f(0) \) is equal to

For what value of \(x\), the function \(2x^3+3x^2-36x+10\) has minimum?

For what value of \(x\), the function \(2x^3+3x^2-36x+10\) has minimum?

If a quadratic function in \( x \) has the value 19 when \( x = 1 \) and has a maximum value 20 when \( x = 2 \), then the function is

Quadrilateral PQRS is inscribed inside a rectangle of dimensions \( 10 \, \text{cm} \times 8 \, \text{cm} \). The value of \( x \), if the area of the quadrilateral is minimum, is

A solid \(S\) is made from a cylinder surmounted by a hemisphere on top with both its circular faces sharing a common centre. The radius of cylinder and radius of hemisphere are \(x\) cm. The height of the cylinder is \((20-4x)\) cm and the volume of \(S\) is \(V=\frac{1}{3}\pi y\). Find the maximum value of \(y\).

The curve \( ax^3+bx^2+cx+d \) has a point of minima at \( x=1 \), then

Let \(f(x) = e^{x(2x^{2} + ax + 2 - a)}\). If \(f\) has a local minimum at \(x = 2\), the value of \(a\) is equal to

The slope of the curve \( y = -x^3 + 3x^2 + 8x - 20 \) is maximum at:

If \( f(x) = \lfloor x \rfloor \) is the greatest integer function, then the correct statement is:

If surface area \( S \) is constant, the volume \( V = \frac{1}{4}(Sx - 2x^3) \), \( x \) being the edge of the base. Show that the volume \( V \) is maximum for \( x = \frac{\sqrt{6}}{6} \).

Let $ f(x) = |x^2 - 4x + 3| + |x^2 - 5x + 6| $. The minimum value of $ f(x) $ is:

If the expression \(x + \frac{1}{x^2},\; x>0\) attains minimum value at \(x=\alpha\), then \(\alpha^3\) is:

Subject to constraints: 2x + 4y ≤ 8, 3x + y ≤ 6, x + y ≤ 4, x, y ≥ 0; The maximum value of Z = 3x + 15y is: