List of top Mathematics Questions on Increasing and Decreasing Functions

If $f(x) = x^2 + bx + 1$ is increasing in the interval $[1, 2]$, then the least value of $b$ is:

Given: \(5f (x) 4f(\frac 1x) = x^2 - 4 \) & \(y = 9f(x) × x^2\) If y is strictly increasing, then find interval of \(x\).

In which interval the function \(f(x) = \frac {x}{(x^2-6x-16)}\) is increasing?

Let \(f:→R→(0,∞)\) be increasing function such that \(Lt_{x→∞}\frac {f(7x)}{f(x)}=1\), then \(Lt_{x→∞}[\frac {f(5x)}{f(x)}-1]\) is equal to

Let $\alpha \in(0,1)$ and $\beta=\log _e(1-\alpha)$ Let $P_n(x)=x+\frac{x^2}{2}+\frac{x^3}{3}+\ldots+\frac{x^n}{n}, x \in(0,1)$ Then the integral $\int\limits_0^\alpha \frac{t^{50}}{1-t} d t$ is equal to

If the function \(f(x)=\frac{k \sin x+2\cos x}{\sin x+\cos x}\) is increasing for all values of x, then

The interval in which the \(f(x) = sinx-cosx, 0 ≤ x ≤ 2π\) is strictly decreasing is :

The interval in which the function \(f(x) = 10-6x-2x²\) is decreasing is:

The function \(f(x)=sinx+cosx,0\leq x\leq 2\pi \) is :

The value of b for which the function f(x) = sinx - bx + C, where b and e are constants is decreasing for \(x \in R\) is given by

The interval on which the function \(f(x)=2x^3 +12x^2 +18x-7\) is decreasing, is:

The values of b for which the function f(x) = cos x + bx+ a decreases on R are

If \(f(x)=-3x^2\), then f(x) is:

Let \(g : (0, ∞) →R\) be a differentiable function such that \(∫(\frac {x(cos⁡x−sin⁡x)}{e^x+1} + \frac {g(x)(e^x+1−xe^x)}{(e^x+1)2})dx = \frac {xg(x)}{e^x+1}+c,\) for all \(x>0\), where c is an arbitrary constant. Then:

The function f(x)=x⁵e^-x is increasing in the interval

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

The function f(x) = x² - 2x is strictly decreasing in the interval

The interval in which the function $f(x) = x^3 - 6x^2 + 9x + 10$ is increasing in

For $0 \leq p \leq 1$ and for any positive $a, b$ let $I(p) = (a + b)^p, J(p) = a^p + b^p$, then

Consider the following statements in respect of the function $f(x)=x^{3}-1, x \in[-1,1]$ I. $f(x)$ is increasing in $[-1,1]$ II. $f(x)$ has no root in $(-1,1)$. Which of the statements given above is/are correct?

If $A=\left\{x \in R / \frac{\pi}{4} \leq x \leq \frac{\pi}{3}\right\}$ and $f(x)=\sin x-x$, then $f(A)$ is equal to

The equation $x log x = 2 - x$ is satisfied by at least one value of $x$ lying between $1$ and $2$. The function $f(x) = x log x$ is an increasing function in $[1,2]$ and $g (x)=2-x$ is a decreasing function in $[1, 2]$ and the graphs represented by these functions intersect at a point in $[1,2]$

The equation $e ^{4 x}+8 e ^{3 x}+13 e ^{2 x}-8 e ^x+1=0, x \in R$ has :