Prove that the function f(x)= is: Strictly decreasing in (0, ). - Vidyadip

Question

Prove that the function $\text{f}(\text{x})=\cos\text{x}$ is:
Strictly decreasing in $(0,\pi).$

✓

Answer

$\text{f}(\text{x})=\cos\text{x}$
$\text{f}'(\text{x})=-\sin\text{x}$
Here,
$0<\text{x}<\pi$
$\Rightarrow\sin\text{x}>0$ $[\because$ sine function is positive in first and second quadrent$]$
$\Rightarrow-\sin\text{x}<0$
$\Rightarrow\text{f}'(\text{x})<0,\forall\ \text{x}\in(0,\pi)$
So, f(x) is strictly decreasing on $(0,\pi).$

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→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If the tangent to a curve at a point (x, y) is equally inclined to the co-ordinates axes then write the value of $\frac{\text{dy}}{\text{dx}}.$

Evaluate the following:
$\tan\Big(\cos^{-1}\frac{8}{17}\Big)$

If $A = \{1, 2, 3\}$ and $B = \{a, b\},$ write the total number of functions from $A$ to $B.$

Find the principal value of the following:
$\cos^{-1}\Big(\sin\frac{4\pi}{3}\Big)$

Evaluate the following determinant:
$\begin{vmatrix}\text{x}&-7\\\text{x}&5\text{x}+1 \end{vmatrix}$

Write a square matrix which is both symmetric as well as skew$-$symmetric.

Find the components along the coordinate axis of the position vector of the following point:S(4,-3)

Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.

If $f : R \rightarrow R$ be defined by $f(x) = x^4,$ write $f^{-1}(1).$

A man $1.6m$ tall walks at the rate of $0.3 \ m/s$ away from a street light is $4 m$ above the ground. At what rate is the tip of his shadow moving? At what rate is his shadow lengthening?