(D) Given the function $y = x^4$.Find the derivative with respect to $x$: $\frac{dy}{dx} = 4x^3$.For the function to be increasing,$\frac{dy}{dx} > 0$

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Increasing in $(0, \infty)$ and decreasing in $(-\infty, 0)$

(D) Given the function $y = x^4$.Find the derivative with respect to $x$: $\frac{dy}{dx} = 4x^3$.For the function to be increasing,$\frac{dy}{dx} > 0$,which implies $4x^3 > 0$,so $x > 0$.Thus,the function is increasing in the interval $(0, \infty)$.For the function to be decreasing,$\frac{dy}{dx} Thus,the function is decreasing in the interval $(-\infty, 0)$.

Class 12 Mathematics Applications of Derivatives Increasing and Decreasing function

Medium

What type of function is $y = x^4$?

A
Strictly increasing
B
Strictly decreasing
C
Decreasing in $(0, \infty)$ and increasing in $(-\infty, 0)$
D
Increasing in $(0, \infty)$ and decreasing in $(-\infty, 0)$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

Applications of Derivatives

Subtopic

Increasing and Decreasing function

If $f(x) = x + \log \left( \frac{x-1}{x+1} \right)$ is a well-defined real-valued function, then $f$ is

MediumTS EAMCET 2025

View Solution

Let $f(x) = \int \frac{x^2-3x+2}{x^4+1} \, dx$. Then the function decreases in the interval:

MediumMHT CET 2023

View Solution

Let $f(x)=3 \sin ^{4} x+10 \sin ^{3} x+6 \sin ^{2} x-3$,where $x \in\left[-\frac{\pi}{6}, \frac{\pi}{2}\right]$. Then,$f$ is $.....$

DifficultJEE MAIN 2021

View Solution

For what values of $a$ is the function $f$ given by $f(x) = x^2 + ax + 1$ increasing on the interval $[1, 2]$?

EasyGSEB 2016

View Solution

If $f(x) = \frac{a \sin x + b \cos x}{c \sin x + d \cos x}$ is decreasing for all $x$,then

MediumMHT CET 2024

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

What type of function is $y = x^4$?

Similar Questions

If $f(x) = x + \log \left( \frac{x-1}{x+1} \right)$ is a well-defined real-valued function, then $f$ is

Let $f(x) = \int \frac{x^2-3x+2}{x^4+1} \, dx$. Then the function decreases in the interval:

Let $f(x)=3 \sin ^{4} x+10 \sin ^{3} x+6 \sin ^{2} x-3$,where $x \in\left[-\frac{\pi}{6}, \frac{\pi}{2}\right]$. Then,$f$ is $.....$

For what values of $a$ is the function $f$ given by $f(x) = x^2 + ax + 1$ increasing on the interval $[1, 2]$?

If $f(x) = \frac{a \sin x + b \cos x}{c \sin x + d \cos x}$ is decreasing for all $x$,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module