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 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 = $: