Determine whether f(x)=- 2 + is a increasing or decreasing on (- … - Vidyadip

Question

Determine whether $\text{f}(\text{x})=\frac{-\pi}{2}+\sin\text{x}$ is a increasing or decreasing on $\Big(\frac{-\pi}{3},\frac{\pi}{3}\Big).$

✓

Answer

$\text{f}(\text{x})=\frac{-\pi}{2}+\sin\text{x}$
$\text{f}'(\text{x})=\frac{-1}{2}+\cos\text{x}$
Here,
$\frac{-\pi}{3}<\text{x}<\frac{\pi}{3}$
$\Rightarrow\cos\text{x}>\frac{1}{2}$
$\Rightarrow\frac{-1}{2}+\cos\text{x}>0$
$\Rightarrow\text{f}'(\text{x})>0,\forall\ \text{x}\in\Big(\frac{-\pi}{3},\frac{\pi}{3}\Big)$
So, f(x) is increasing on $\Big(\frac{-\pi}{3},\frac{\pi}{3}\Big).$

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 "Solve the Following Question.(3 Marks)" from Increasing and Decreasing Functions→Increasing and Decreasing Functions — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

For the binary operation multiplication modulo $10 (\times _{10})$ defined on the set $S = \{1, 3, 7, 9\},$ write the inverse of $3.$

Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point 'c' in the indicated interval as stated by the Lagrange's mean value theorem.$\text{f}(\text{x})=\sin\text{x}-\sin2\text{x}-\text{x}\text{ on }[0,\pi]$

If $x < 0, y < 0$ such that $xy = 1$, then write the value of $\tan^{-1}x + \tan^{-1}y$.

Find the area of the region bounded by the curves $x^2 = 8y, y = 2, y = 4$ and the $Y-$axis, lying in the first quadrant

Find $\frac{d y}{d x}$ if

$e^{e^{x-y}}=\frac{x}{y}$

Using determinants show that the following points are collinear:
$(5, 5), (-5, 1)$ and $(10, 7)$

Find the values of $x$ for which the function $f(x) = x^3 – 6x^2 – 36x + 7$ is strictly increasing

Reduce each of the following differential equations to the separted variable form and hence find the general solution.$\frac{d y}{d x}=(4 x+y+1)^2$

Find the points o local maxima or local minima, if any, of the following functions, using the first derivatives test. Also, find the local maximum or local minimum values, as the case may be:
$f(x) = (x - 5)^4$

Check whether the relation R defined on the set A = {1, 2, 3, 4, 5, 6} as R = {(a, b): b = a + 1} is reflexive, symmetric or transitive.