(A) To determine the interval where the function $y = f(x) = 6 - 9x - x^2$ is strictly increasing,we find its derivative: $f'(x) = \frac{d}{dx}(6 - 9x

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

(A) To determine the interval where the function $y = f(x) = 6 - 9x - x^2$ is strictly increasing,we find its derivative: $f'(x) = \frac{d}{dx}(6 - 9x - x^2) = -9 - 2x$. For the function to be strictly increasing,we must have $f'(x) > 0$. So,$-9 - 2x > 0$. $-2x > 9$. Dividing by $-2$ reverses the inequality: $x Thus,the function is strictly increasing on the interval $(-\infty, -4.5)$.

Class 12 Mathematics Applications of Derivatives Increasing and Decreasing function

Easy

The function $y = 6 - 9x - x^2$ is strictly increasing on the interval . . . . . . .

GSEB 2024 All GSEB

A
$(-\infty, -4.5)$
B
$(-4.5, \infty)$
C
$(-4.5, 0)$
D
$(0, 4.5)$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

Applications of Derivatives

Subtopic

Increasing and Decreasing function

Previous Year

GSEB 2024 Paper All GSEB years →

If $f(x) = \frac{1}{x + 1} - \log(1 + x)$,where $x > 0$,then what type of function is $f$?

Medium

View Solution

If the function $f(x)=x^3+2 p x^2+27 x+16$ is strictly increasing for all $x \in R$,then the range of $p$ is

EasyAP EAMCET 2018

View Solution

Which of the following is not a decreasing function on the interval $\left( 0, \frac{\pi}{2} \right)$?

Easy

View Solution

The roots of $(x-41)^{49}+(x-49)^{41}+(x-2009)^{2009}=0$ are

KVPY 2010

View Solution

The complete set of values of $m$ for which the function $f(x) = e^{\sin x} + 2m\sin x + 1$ is increasing for all $x \in \left( 0, \frac{\pi}{2} \right)$ is:

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

The function $y = 6 - 9x - x^2$ is strictly increasing on the interval . . . . . . .

Similar Questions

If $f(x) = \frac{1}{x + 1} - \log(1 + x)$,where $x > 0$,then what type of function is $f$?

If the function $f(x)=x^3+2 p x^2+27 x+16$ is strictly increasing for all $x \in R$,then the range of $p$ is

Which of the following is not a decreasing function on the interval $\left( 0, \frac{\pi}{2} \right)$?

The roots of $(x-41)^{49}+(x-49)^{41}+(x-2009)^{2009}=0$ are

The complete set of values of $m$ for which the function $f(x) = e^{\sin x} + 2m\sin x + 1$ is increasing for all $x \in \left( 0, \frac{\pi}{2} \right)$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module