List of top Mathematics Questions on Applications of Derivatives asked in CBSE CLASS XII

If the volume of a solid hemisphere increases at a uniform rate, prove that its surface area varies inversely as its radius.
Find the absolute maximum value of $f(x)=\cos x+\sin^2 x$, where $x\in[0,\pi]$.
Given that \( f(x) = \frac{\log x}{x} \), find the point of local maximum of \( f(x) \).