Find the maximum and minimum value of function f(x)= 2 x+5. - Vidyadip

Question

Find the maximum and minimum value of function $f(x)=\sin 2 x+5$.

✓

Answer

$
\begin{array}{rlrl}
f(x) & =\sin 2 x+5 \\
\because & -1 \leq \sin 2 x \leq 1 \quad \forall x \in R \\
\therefore & -1+5 \leq \sin 2 x+5 \leq 1+5, \quad \forall x \in R \\
\Rightarrow& 4 \leq \sin 2 x+5 \leq 6 \quad \forall x \in R \\
\Rightarrow & 4 \leq f(x) \leq 6 \forall x \in R
\end{array}
$
hence maximum value is 6 and minimum value is 4 .

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 Applications of Derivative→Applications of Derivative — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $\vec{\text{a}}$ and $\vec{\text{b}}$ are unit vectors, find the angle between $\vec{\text{a}}+\vec{\text{b}}$ and $\vec{\text{a}}-\vec{\text{b}}.$

Find $\vec{\text{a}}.\vec{\text{b}}$ when
$\vec{\text{a}}=\hat{\text{j}}+2\hat{\text{k}}$ and $\vec{\text{b}}=2\hat{\text{i}}+\hat{\text{k}}$

An urn contains 5 red and 2 black balls. Two balls are randomly drawn. Let X represent the number of black balls. What are the possible values of X? Is X a random variable ?

If the points $(a, 0), (0, b)$ and $(1, 1)$ are collinear, prove that $a + b = ab.$

Write the value of $\hat{\text{i}}.\big(\hat{\text{j}}\times\hat{\text{k}}\big)+\hat{\text{j}}.\big(\hat{\text{k}}\times\hat{\text{i}}\big)+\hat{\text{k}}.\big(\hat{\text{j}}\times\hat{\text{i}}\big).$

If $-\frac{\pi}{2}<\text{x}<0\text{ and y}=\tan^{-1}\sqrt{\frac{1-\cos2\text{x}}{1+\cos2\text{x}}},$ find $\frac{\text{dy}}{\text{dx}}.$

Three shopkeepers A, B and C go to a store to buy stationary. A purchases 12 dozen notebooks, 5 dozen pens and 6 dozen pencils. B purchases 10 dozen notebooks, 6 dozen pens and 7 dozen pencils. Cpurchases 11 dozen notebooks, 13 dozen pens and 8 dozen pencils. A notebook costs 40 paise, a pen costs Rs. 1.25 and a pencil costs 35 paise. Use matrix multiplication to calculate each individual's bill.

A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event the number is even, and B be the event the number is red. Are A and B independent?

If the equations of a line AB are $\frac{3-\text{x}}{1}=\frac{\text{y}+2}{-2}=\frac{\text{z}-5}{4},$ write the direction ratios of a line parallel to AB.

Determine whether or not the definition of $*$ given below gives a binary operation. In the event that $*$ is not a binary operation give justification of this.
On $Z^+,$ defined $*$ by $a * b = a - b.$
Here, $Z^+$ denotes the set of all non$-$negative integers.