List of top Mathematics Questions on Maxima and Minima

The maximum volume (in cu. m) of a right circular cone having slant height \(3\) m is

If \[ u=\sqrt{a^2\cos^2\theta+b^2\sin^2\theta} + \sqrt{a^2\sin^2\theta+b^2\cos^2\theta}, \] then the difference between the maximum and minimum values of \(u^2\) is

The maximum area of a rectangle inscribed in a circle of radius $r$ is:

The minimum value of the function $f(x) = x^2 + \frac{250}{x}$ for $x > 0$ is:

The maximum value of $y = x(\log x)^2$ is:

If \(m\) and \(M\) are respectively the absolute minimum and absolute maximum values of the function \[ f(x)=|2x^2-x-6|+2x-3 \] in the interval \([-2,4]\), then \(2M+8m=\)

If \[ y=a\log|x|+bx^2+x \] has its extremum values at \[ x=-1 \quad\text{and}\quad x=2, \] then \((a,b)=\)

On the interval \([0,1]\), the function \(f(x) = x^{25}(1-x)^{75}\) attains its maximum value at the point \(x =\)....

The value of \(x\) so that the volume of the parallelopiped formed by the vectors \(\hat{i}+x\hat{j}+\hat{k}\), \(\hat{j}+x\hat{k}\) and \(x\hat{i}+\hat{k}\) is minimum, is

A tank with a rectangular base and rectangular sides, open at the top is made. Depth of the tank is \(4\) m and its volume is \(36\) cubic meters. For making a tank cost of base material used is Rs. \(100\) per sq. meter and that of sides is Rs. \(50\) per sq. meter. Then minimum cost of tank is ..............

The equation of the tangent to the curve \(y = \sqrt{9-3x^2}\) at the point where the ordinate and abscissa equal is...

The number 28 is divided into two positive parts such that the sum of the cube of one part and the square of the other part is minimum, then the absolute difference between the two parts is

A cylindrical tank without a top lid is being manufactured to hold a fixed volume of \(125π\) cubic cm. The minimum surface area required to construct this tank is ............square cm

The minimum value of \(\frac{logx}{x}\) in the interval \((2,\infty )\) is

A ball is thrown in the air. Its height at any time \(t\) is given by \(h = 3+14t-5t^2\), then the maximum height it can reach

The maximum value of \((\frac{1}{x})^x\), \(x > 0\) is

Let \(x_0\) be the point of local maxima of \(f(x) = \overset{̄}{a}\cdot (\overset{̄}{b}\times \overset{̄}{c})\) where \(\overset{̄}{a} = x\hat{i}-2\hat{j}+3\hat{k},\overset{̄}{b} = -2\hat{i}+x\hat{j}-\hat{k}\) and \(\overset{̄}{c} = 7\hat{i}-2\hat{j}+x\hat{k}\) then the value of \(\overset{̄}{a}\cdot \overset{̄}{c}\) at \(x = x_0\) is

The difference between the local extreme values of the function \(f(x) = 2x^3-15x^2+36x+40\) is ......

A wire of length \(64\) m is to be bent to form a rectangle such that its area is maximum, then its area is.....

Let \[ f(x)=x^3-\frac32x^2, \] which of the following is not correct?

Let \[ f(x)=x^3-\frac32x^2, \] which of the following is not correct?

Let $f(x) = \sin x \sin(x + \frac{\pi}{3}), x \in \mathbb{R}$. Then the minimum value of $f$ is equal to

If the maximum value of the function $f(x) = \alpha - 4x - x^2$ is 1, then the value of $\alpha$ is equal to

If \(f(x) = x - 7, g(x) = 11 - x\), and \(h(x) = f(x)g(x)\), then the maximum value of \(h\) is