List of top Mathematics Questions on Increasing and Decreasing Functions asked in KEAM

Let $f$ and $g$ be differentiable real valued functions on $[0,\infty)$. If $f$ is increasing, $g$ is decreasing and $h(x)=f(g(x))$, then $h(2026)-h(2025)$ is

The function $f(\theta)=\sin \theta+\cos \theta,\ 0\leq \theta \leq 2\pi$ is decreasing in the interval:

The function $f(x)=e^x-x$ is increasing in the interval:

The function \( f(x) = 2x^3 - 3x^2 - 36x + 28 \) is increasing in

The function \( f(x) = x^2(x-2) \) is strictly decreasing in

If $y = 8x^3 - 60x^2 + 144x + 27$ is a strictly decreasing function in the interval:

The function \( f(x) = \sin x - kx - c \), where \( k \) and \( c \) are constants, decreases always when

The function \( f(x) = 2x^3 - 15x^2 + 36x + 6 \) is strictly decreasing in the interval:

The function \( f(x) = 2x^3 - 15x^2 + 36x + 6 \) is strictly decreasing in the interval:

The function \( f(x) = 2x^3 - 15x^2 + 36x + 6 \) is strictly decreasing in the interval: