Find the intervals in which the following functions are increasin… - Vidyadip

Question

Find the intervals in which the following functions are increasing or decreasing.
$f(x) = x^2+ 2x - 5$

✓

Answer

We have,
$f(x) = x^2+ 2x - 5$
$\therefore$$ f'(x) = 2x + 2$
Now.
$f'(x) = 0 $
$\Rightarrow x = -1$
Point x = -1 divides the real line into two disjoints intervals i.e., $(-\infty,-1)$ and $(-1,\infty).$
In interval $(-\infty,-1),$
$f'(x) = 2x + 2 < 0.$
$\therefore$ f is strictly decreasing in interval $(-\infty,-1).$
Thus, f is strictly decreasing for $x < -1.$
In interval $(-1,\infty),$
$f'(x) = 2x + 2 > 0.$
$\therefore$ f is strictly increasing in interval $(-1,\infty).$
Thus, f is strictly increasing for $x > -1.$

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 "Solve the Following Question.(5 Marks)" from Increasing and Decreasing Functions→Increasing and Decreasing Functions — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Find the area included between the parabolas $y^2 = 4ax$ and $x^2 = 4 by$.

Prove that:$\int\limits^\pi_0\text{xf}(\sin\text{x})\text{dx}=\frac{\pi}{2}\int\limits^\pi_0\text{f}(\sin\text{x})\text{dx}$

How should we choose two numbers, each greater than or equal to −2, whose sum so that the sum of the first and the cube of the second is minimum?

Solve the following systems of linear equations by cramer's rule:

$x + y + z + w = 2,$

$x - 2y + 2z + 2w = -6,$

$2x + y - 2z + 2w = -5,$

$3x - y + 3z - 3w = -3$

Solve the following systems of homogeneous linear equations by matrix method:

$x + y - z = 0$

$x - 2y + z = 0$

$3x + 6y - 5z = 0$

Evalute the following integrals:
$\int\frac{\sin(\text{x}-\alpha)}{\sin(\text{x}+\alpha)}\text{dx}$

Show that the vectors $\vec{\text{a}},\ \vec{\text{b}},\ \vec{\text{c}}$ given by $\vec{\text{a}}=\hat{\text{i}}+2\hat{\text{j}}+3\hat{\text{k}},\ \vec{\text{b}}=2\hat{\text{i}}+\hat{\text{j}}+3\hat{\text{k}}$ and $\vec{\text{c}}=\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$ are non-coplanar. Express vector $\vec{\text{d}}=2\hat{\text{i}}-\hat{\text{j}}-3\hat{\text{k}}$ as a linear combination of the vectors $\vec{\text{a}},\ \vec{\text{b}}\text{ and }\vec{\text{c}}$.

Prove that the area the first quadeant enclosed by the x-axis, the line $\text{x}=\sqrt{3}\text{y}$ and the circle is $\frac{\pi}{3}$ .

If $\text{x}\sin(\text{a}+\text{y})+\sin\text{a}\cos(\text{a}+\text{y})=0,$ prove that $\frac{\text{dy}}{\text{dx}}=\frac{\sin^2(\text{a}+\text{y})}{\sin\text{a}}$

Differentiate the following functions with respect to x:
$\tan^{-1}\Big(\frac{\text{a}+\text{b}\tan\text{x}}{\text{b}-\text{a}\tan\text{x}}\Big)$