Show that f(x)=x^2-x is an increasing function on (0, 2 ). - Vidyadip

Question

Show that $\text{f}(\text{x})=\text{x}^2-\text{x}\sin\text{x}$ is an increasing function on $\Big(0,\frac{\pi}{2}\Big).$

✓

Answer

We have,
$\text{f}(\text{x})=\text{x}^2-\text{x}\sin\text{x}$
$\therefore\ \text{f}'(\text{x})=2\text{x}-\sin\text{x}-\text{x}\cos\text{x}$
Now,
$\text{x}\in\Big(0,\frac{\pi}{2}\Big)$
$\Rightarrow0\leq\sin\text{x}\leq1,0\leq\cos\text{x}\leq1$
$\Rightarrow2\text{x}-\sin\text{x}-\text{x}\cos\text{x}>0$
$\Rightarrow\text{f}'(\text{x})\geq0$
So, f(x) is strictly increasing function on $\Big(0,\frac{\pi}{2}\Big).$

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.(2 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

Integrate the following functions w.r.t x:

$\frac{\cos x}{\sin (x-a)}$

Find $k$, such that the function
$
P (x)=\left\{\begin{array}{ll}
k\left(\frac{4}{x}\right) & ; \quad x=0,1,2,3,4, k>0 \\
0 ; & \text { otherwise, }
\end{array}\right.
$
is a probability mass function (p.m.f.)

On expanding by first row, the value of the determinant of $3 \times 3$ square matrix $A=\left[a_{i j}\right]$ is $a_{11} C_{11}+a_{12} C_{12}+a_{13} C_{13}$, where $\left[C_{i j}\right]$ is the cofactor of $a_{i j}$ in A . Write the expression for its value on expanding by second column.

Evaluate the following integrals:
$\int\text{x}^{\frac{5}{4}}\text{dx}$

Integrate the following functions w.r.t. x:

$\frac{1}{4 x+5 x^{-11}}$

Evaluate the following integrals:
$\int\bigg\{\text{x}^2+\text{e}^{\log\text{x}}+\Big(\frac{\text{e}}{2}\Big)^\text{x}\bigg\}\text{dx}$

Find the equation of tangent to the curve $y=x^2+4 x+1$ at $(-1,-2)$.

Integrate the following functions w. r. t. x

$\int \frac{1}{3-2 \cos 2 x} \cdot d x$

Evaluate the following : $\int \frac{1}{\sqrt{3 x+1}-\sqrt{3 x-5}} \cdot d x$

Let $R_0$ denote the set of all non-zero real numbers and let $A=R_0 \times R_0$.
If ' $k$ ' is a binary operation on adefined by, $(a, b)^*(c, d)=(a c, b d)$ for all $(a, b),(c, d) \in A$
Find the identity element in A