Increasing and Decreasing Functions

The intervals in which the function f given by f (x) = x² – 4x + 6 is increasing is

• $\left(-\infty,\ 2\right)$

• $\left(2,\ \infty\right)$

• $\left(-\infty,\ \infty\right)$

• none of these

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

Intervals in which the function given by $f\left(x\right)=\sin3x$ ,  $x\in\left[0,\ \frac{\pi}{2}\right]$ is decreasing

•  $\left(\frac{\pi}{6},\ \frac{\pi}{2}\right]$  

•  $\left[0,\ \frac{\pi}{6}\right)$  

•  $\left[0,\ \frac{\pi}{3}\right)$  

•  $\left(\frac{\pi}{3},\ \frac{\pi}{2}\right]$  

Tags

CCSS.HSF.TF.A.4

The logarithmic function is increasing on

• $\left(0,\ 1\right)$

• $\left(0,\ \infty\right)$

• $\left(1,\ \infty\right)$

• $\left(-\infty,\ \infty\right)$

Tags

CCSS.HSF-IF.C.7E

In the interval (- 1, 1), function f given by $f(x)=x^2–\ x+1$  is

• increasing

• decreasing

• increasing and decreasing both

• neither increasing nor decreasing

The interval in which $y=x^2e^{–x}$  is increasing is

•  $\left(-2,\ 0\right)$  

•  $\left(-\infty,\ \infty\right)$  

•  $\left(2,\ \infty\right)$  

•  $\left(0,\ 2\right)$  

The function f (x) = tan x – 4x is strictly decreasing on

• $\left(-\frac{\pi}{3},\ \frac{\pi}{3}\right)$

• $\left(\frac{\pi}{3},\ \frac{\pi}{2}\right)$

• $\left(-\frac{\pi}{2},\ -\frac{\pi}{3}\right)$

• none of these

Tags

CCSS.HSF.TF.A.4

Intervals in which the function $y=x^4-\frac{4x^3}{3}$  is strictly increasing is 

•  $\left(1,\ \infty\right)$  

•  $\left(-\infty,\ 0\right)$  

•  $\left(0,\ 1\right)$  

• none of these

The interval on which the function f (x) = 2x³ + 9x² + 12x – 1 is decreasing is:

• $\left[-1,\ \infty\right)$

• $\left[-2,\ -1\right]$

• $\left(-\infty,\ -2\right]$

• $\left[-1,\ 1\right]$

Tags

CCSS.HSA.APR.B.3

y = x (x – 3)² decreases for the values of x given by :

• $1<x<3$

• $x<0$

• $x>0$

• $0<x<\frac{3}{2}$

Which of the following functions is decreasing on $\left(0,\ \frac{\pi}{2}\right)$  

•  $\sin2x$  

•  $\tan x$  

•  $\cos x$  

•  $\cos3x$  

Tags

CCSS.HSF.TF.A.4