Test whether the function f(x) = x^3 + 6x^2 + 12x − 5 is increasi… - Vidyadip

Question

Test whether the function $f(x) = x^3 + 6x^2 + 12x − 5$ is increasing or decreasing for all $x \in R$

✓

Answer

$f(x)=x^3+6 x^2+12 x-5 \therefore f^{\prime}(x)=3 x^2+12 x+12$
$=3\left(x^2+4 x+4\right)$
$=3(x+2)^2$
$3(x+2)^2 \text { is always positive for } x \neq-2$
$\therefore f^{\prime}(x) \geq 0 \text { for all } x \in R$
Hence, $f(x)$ is an increasing function for all $x \in R$.

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.(2 Marks)" from Question Bank [2022]→Question Bank [2022] — 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 general solution of :$\cos \theta=-\frac{1}{2}$

Let $R=\left\{\left(a, a^3\right)\right.$ : $a$ is a prime number less than 5$\}$ be a relation. Find the range of $R$.

Evaluate: $\int \log x d x$

If $\vec{\text{a}}=\hat{\text{i}}+2\hat{\text{j}}-3\hat{\text{k}}$ and $\vec{\text{b}}=2\hat{\text{i}}+4\hat{\text{j}}+9\hat{\text{k}}$, find a unit vector parallel to $\vec{\text{a}}+\vec{\text{b}}$.

Find the cartesian form of the equation of a plane whose vector equation is:
$\vec{\text{r}}\cdot\big(-\hat{\text{i}}+\hat{\text{j}}+2\hat{\text{k}}\big)=9$

An urn contains 7 red and 4 blue balls. Two balls are drawn at random with replacement. Find the probability of getting,
2 Blue balls.

Evaluate the following : $\int \frac{\cos x-\cos 2 x}{1-\cos x} \cdot d x$

Determine whether the following operations define a binary operation on the given set or not:$'\odot'$ on N defined by $\text{a}\odot\text{b}=\text{a}^{\text{b}}+\text{b}^{\text{a}}$ for all $\text{a, b}\in\text{N.}$

If $\pi\leq\text{x}\leq3\pi$ and $\text{y}=\cos^{-1}(\cos\text{x}),$ find $\frac{\text{dy}}{\text{dx}}.$

Differentiate the following w.r.t. x :

$\frac{3}{5 \sqrt[3]{\left(2 x^2-7 x-5\right)^5}}$