Find the maximum and minimum values, if any, of the function give… - Vidyadip

Question

Find the maximum and minimum values, if any, of the function given by:
f(x) = |sin 4x + 3|

✓

Answer

Given: $\text{f}\text{(x)} = |\sin 4\text{x} + 3|$
Since $-1\leq\sin 4\text{x}\leq 1\text{ for all }\text{x} \in \text{R}$
Adding 3 to all sides, $-1+3 \leq \sin 2\text{x}+5 \leq 1+3\ \Rightarrow \ 2\leq \text{f}\text{(x)}\leq4$
Therefore, minimum value of f(x) is 2 and maximum 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 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

Let $R$ = {$(x, y): |x^2 - y^2| < 1$} be a relation on set $A$ = {$1, 2, 3, 4, 5$}. Write $R$ as a set of ordered pairs.

Evaluate the following integrals:
$\int\limits^{\text{e}^2}_\text{e}\frac{1}{\text{x}\log\text{x}}\text{ dx}$

Evaluate the definite integral $\int\limits_0^{\frac{\pi }{2}} {{{\cos }^2}x dx} $

If f(x) attains a local minimum at x = c, then write the values of f' (c) and f'' (c).

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

Write the value of $\cos\Big(2\sin^{-1}\frac{1}{2}\Big).$

Three numbers are chosen from 1 to 20. Find the probability that they are consecutive.

What are the direction cosines of Y-axis?

Find a unit vector perpendicular to each of the vector $\vec{a}+\vec{b}\ \text{and}\ \vec{a}-\vec{b},\ \text{where}$ $\vec{a}=3\hat{i}+2\hat{j}+2\hat{k}\ \text{and}\ \vec{b}=\hat{i}+2\hat{j}-2\hat{k}.$

What happens to a function f(x) at x = a, if $\lim\limits_{{\text{x}}\rightarrow\text{a}}\text{f(x})=\text{f}(\text{a})?$