List of top Mathematics Questions on Applications of Derivatives asked in KEAM

The point \(P\) lies on the curve with equation \[ y = x\sqrt{2\log_e(x)}, \qquad x>0. \] If \[ \frac{dy}{dx}=2 \] at \(x=k\), then the value of \(k\) is equal to: 

Let $f(x)=10x^2+ax,\; x\in \mathbb{R}$ be such that $a^2-400<0$. Let $g(x)=f(x)+f'(x)+f''(x)$. Then $g(x)$ is:
The distance travelled by a moving particle is given by $s=\frac{t^{2}}{2}-6t+8$, where $t$ denotes the time in seconds. The velocity becomes zero when $t$ is equal to: