List of top Mathematics Questions on Differential Calculus asked in AP EAPCET

Let $f:\mathbb{R}^{+}\rightarrow\mathbb{R}$ be such that $f(e)=\frac{7}{4}$ and $f^{\prime}(x^{2})=\frac{3\log x}{x^{2}}$, then $f(e^{2})=$

The value of \(c\) of Lagrange's Mean Value Theorem for \[ f(x)=\sqrt{25-x^2} \] on \([1,5]\) is:

Let \[ f(x)=x^2+\frac{1}{x^2} \] and \[ g(x)=x-\frac{1}{x} \] for \(x\in \mathbb{R}-\{-1,0,+1\}\), then the local minimum of \[ \frac{f(x)}{g(x)} \] is