List of top Mathematics Questions on Application of derivatives asked in KEAM

The function $f(x)=2x^{3}-15x^{2}+36x-24$ is strictly decreasing in the interval is

The distance $s$ in meters travelled by a particle in $t$ seconds is given by $s=e^{t}(4\cos 3t+5\sin 3t)$. Then the velocity of the particle at time $t$ is given by

Let $f(x) = 1 + x\log\left(x + \sqrt{x^2+1}\right) - \sqrt{x^2+1}, \; x \geq 0$. Then:

Let \( f(x) = (\cos^2 x)(a + \cos x) \). If \( f'\left(\frac{\pi}{3}\right) = 0 \), then the value of \( a \) is equal to

The function \(f(x) = 2\cos x - x + 3\) is

A point of inflection of the curve given by $y = x^3 - 6x^2 + 12x + 50$ occurs when

The slope of the curve $y = e^x \cos x$, $x \in (-\pi, \pi)$ is maximum at: