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

If the expression \(x + \frac{1}{x^2},\; x>0\) attains minimum value at \(x=\alpha\), then \(\alpha^3\) is:
The function \(\sin x(1+\cos x)\), \(0 \le x \le \pi/2\), has maximum value when \(x\) is
If \( f(x) = \begin{cases} \sin\left(\frac{\pi x}{2}\right), & x<1 \\ 3 - 2x, & x \ge 1 \end{cases} \), then \( f(x) \) has:
The minimum value of \( \frac{x}{\log x} \) is
The minimum radius vector of the curve \( \frac{a^2}{x^2} + \frac{b^2}{y^2} = 1 \) is of length
\( f(x)= \begin{cases} |x^3 + x^2 + 3x + \sin x|\left(3 + \sin\frac{1}{x}\right), & x\neq 0 \\ 0, & x=0 \end{cases} \) The number of points, where \( f(x) \) attains its minimum value, is
The point in the interval [0, 2π], where $f(x)=eˣsin~x$ has maximum slope, is
The maximum value of \( \frac{\log x}{x}, \; 0 < x < \infty \) is
The function $f(x) = x^3 + ax^2 + bx + c, a^2 \le 3b$ has
The maximum value of $f(x) = \frac{\log x{x}$ occurs at $x = $: