Prove that the function f(x)= is: Neither increasing nor decreasi… - Vidyadip

Question

Prove that the function $\text{f}(\text{x})=\cos\text{x}$ is:
Neither increasing nor decreasing in $(0,2\pi)$

✓

Answer

$\text{f}(\text{x})=\cos\text{x}$
$\text{f}'(\text{x})=-\sin\text{x}$
$\Rightarrow\text{f}'(\text{x})<0,\forall\ \text{x}\in(0,\pi)\ ....(1)$
$\Rightarrow\text{f}'(\text{x})>0,\forall\ \text{x}\in(\pi,2\pi)\ ....(2)$
From eqs. (1) and (2), we get
f(x) is strictly decreasing on $(0,\pi)$ and is strictly increasing on $(\pi,2\pi).$
So, f(x) Neither increasing nor decreasing on $(0,2\pi).$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Increasing and Decreasing Functions→Increasing and Decreasing Functions — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If A is a square matrix of order n × n such that |A| = λ, then write the value of |-A|.

Express matrix as the sum of a symmetric and a skew-symmetric matrix: $\left[\begin{array}{ccc} {6} & {-2} & {2} \\ {-2} & {3} & {-1} \\ {2} & {-1} & {3} \end{array}\right]$

If A and B are two independent events such that P(A) = 0.3 and $=0.8\text{P}(\text{A}\cap\overline{\text{B}})$ Find P(B).

Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\text{y}\frac{\text{d}^2\text{x}}{\text{dy}^2}=\text{y}^2+1$

If $\vec{\text{a}}=\hat{\text{i}}+2\hat{\text{j}}-3\hat{\text{k}}$ and $\vec{\text{b}}=2\hat{\text{i}}+4\hat{\text{j}}+9\hat{\text{k}}$, find a unit vector parallel to $\vec{\text{a}}+\vec{\text{b}}$.

For what value of x, the following matrix is singular?
$\begin{vmatrix}5-\text{x}&\text{x}+1\\2&4\end{vmatrix}$

Evaluate the following:
$\sec^{-1}\Big(\sec\frac{25\pi}{6}\Big)$

If f : R → R be defined by $\text{f(x)} = (3 - \text{x}^3)^\frac{1}{3},$ then find fof(x).

Write two different vectors having same direction.

$\text{Find}\ |\vec{a}\ \times\vec{b}|,\ \text{if}\ \vec{a}=\hat{i}-7\hat{j}+7\hat{k}\ \text{and}\ \vec{b}=3\hat{i}-2\hat{j}+2\hat{k}.$