List of top Mathematics Questions on Maxima and Minima asked in KEAM

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

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 $f(x)=2x^{3}-3x^{2}-\lambda x+1, x\in[0,3]$ 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 maximum value of the function $f(x)=x\sqrt{4x-x^{2}}$ is ________.

The minimum of $f(x)=|x+2|$, $x\in\mathbb{R}$ occurs at ________.

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

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 maxima and minima of the function $2x^3 - 15x^2 + 36x + 10$ occur respectively at

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

The minimum value of \( f(x) = \max\{x, 1+x, 2-x\} \) is

The minimum value of \( f(x) = \max\{x, 1+x, 2-x\} \) is

The minimum value of \( f(x) = \max\{x, 1+x, 2-x\} \) is

Maximum value of \( 2x^3 -15x^2 +36x +4 \)

The minimum value of \( f(x) = \max\{x, 1+x, 2-x\} \) is

Let \( a, a + r \) and \( a + 2r \) be positive real numbers such that their product is 64. Then the minimum value of \( a + 2r \) is equal to:

Let \( f(x) = 2x^3 - 9ax^2 + 12a^2x + 1 \), where \( a > 0 \). The minimum of \( f \) is attained at a point \( q \) and the maximum is attained at a point \( p \). If \( p^3 = q \), then \( a \) is equal to:

The minimum value of the function \( \max\{x, x^2\} \) is equal to:

The minimum value of $2x^3 - 9x^2 + 12x + 4$ is: