List of top Mathematics Questions on Maxima and Minima asked in COMEDK UGET

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

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