Is function cos x decreasing on (0, 2 )? - Vidyadip

Question

Is function cos x decreasing on ($0, \frac{\pi}{2}$)?

✓

Answer

Let $f_1(x) = cos x$
$\therefore$ $\mathrm{f}_{1}^{\prime}(\mathrm{x})$ = -sin x
In interval $\left(0, \frac{\pi}{2}\right)$, $\mathrm{f}_{1}^{\prime}(\mathrm{x})$ = -sin x < 0.
Therefore, $f_1(x)$ = cos x is strictly decreasing in interval $\left(0, \frac{\pi}{2}\right)$.

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 "1 Marks Question" from Application of Derivatives→Application of Derivatives — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Discuss the continuity of the function: f(x) = sin x + cos x

Construct a $2\times 2$ matrix $A = [a_{ij}]$ whose element $a_{ij}$ is given by: $\frac{(i+j)^{2}}{2}$

Integrate the function $x \tan^{-1}x$

If $\begin{vmatrix} 3 \text{x}& 7 \$0.3em] -2 & 4\$0.3em] \end{vmatrix} = \begin{vmatrix} 8 & 7 \$0.3em] 6 & 4\$0.3em] \end{vmatrix}, $find the value of x.

If $\left|\begin{array}{cc}3 x & 7 \\ -2 & 4\end{array}\right|=\left|\begin{array}{ll}8 & 7 \\ 6 & 4\end{array}\right|$ then find the value of $x$.

$\text{Find}\ \lambda\ \text{if}\ (2\hat{\text{i}}+6\hat{\text{j}}+14\hat{\text{k}})\times(\hat{\text{i}}-\lambda\hat{\text{i}}+7\hat{\text{k}})=\overrightarrow{0}\dot{}$

Find the area of the region bounded by the curve $y=\cos x$ and the $x$-axis when $0 \leq x \leq \pi$.

Write a vector of magnitude 15 units in the direction of vector.

Write the degree of the differrntial equation $\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}+\Big(\frac{\text{dy}}{\text{dx}}\Big)^{\frac{1}{4}}+\text{x}^{\frac{1}{5}}=0.$

Show that the function f given by $f(x) = \tan^{–1} (sin x + cos x), x > 0$ is always an increasing function in $\left(0, \frac{\pi}{4}\right)$