Find the interval in function 6 - 9x - x2 is increasing or decrea… - Vidyadip

Question

Find the interval in function 6 - 9x - x²is increasing or decreasing.

✓

Answer

It is given that function f(x) = 6 - 9x - x²
f'(x) = -9 - 2x
If f'(x) = 0,
$\Rightarrow x=\frac{-9}{2}$
So, the point x = $\frac{-9}{2}$ divides the real line two disjoint intervals, $\left(-\infty, \frac{-9}{2}\right)$ and $\left(\frac{-9}{2}, \infty\right)$
So, in interval $\left(-\infty, \frac{-9}{2}\right)$
f'(x) = -9 - 2x > 0
Therefore, the given function 'f' is strictly increasing for x < $\frac{-9}{2}$.
And in interval $\left(\frac{-9}{2}, \infty\right)$
f'(x) = -9 - 2x < 0
Therefore, the given function 'f' is strictly decreasing for $x>\frac{-9}{2}$
Thus, f is strictly decreasing for $x>\frac{-9}{2}$

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 "1 Marks" 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

Find the principal value of $\sin ^ { - 1 } \left( - \frac { 1 } { 2 } \right).$

Examine that $\sin \left| x \right|$ is a continuous function.

If R = {(x, y) : x + 2y = 8} is a relation on N, write the range of R.

$\cos^{-1}\bigg(\cos\frac{7\pi}{6}\bigg)$ is equal to:

$\frac{7\pi}{6}$
$\frac{5\pi}{6}$
$\frac{\pi}{3}$
$\frac{\pi}{6}$

Evaluate $\int_{-1}^{1} 5 x^{4} \sqrt{x^{5}+1} d x$

Find the order and degree, if defined, of the differential equation $y^{\prime \prime \prime}+y^{2}+e^{y^{\prime}}=0$

Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\text{y}=\text{px}+\sqrt{\text{a}^2\text{p}^2+\text{b}^2},$ where $\text{p}=\frac{\text{dy}}{\text{dx}}$

Examine if Rolle’s theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle’s theorem from these example?

$\text{f(x)}=[\text{x}]\text{ for x}\in[5,\ 9]$

$\text{Find}\ \lambda\ \text{if}\ (2\hat{\text{i}}+6\hat{\text{j}}+14\hat{\text{k}})\times(\hat{\text{i}}-\lambda\hat{\text{i}}+7\hat{\text{k}})=\overrightarrow{0}\dot{}$

Integrate the function $\frac{\sin x}{\sin (x-a)}$