Download App

Application of Derivatives — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSApplication of Derivatives1 Mark
Question
$2 x^3-6 x+5$ is an increasing function, if
✓

Answer

$(c) :$ Let $f(x)=2 x^3-6 x+5$
On differentiating $\text{w.r.t. x}$, we get $f^{\prime}(x)=6 x^2-6$
Since, it is increasing function.
$\Rightarrow 6 x^2-6 > 0$
$\Rightarrow(x-1)(x+1)>0$
$\Rightarrow x > 1 \text { or } x<-1$

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 "M.C.Q (1 Marks)" from Application of Derivatives→Application of Derivatives — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

The ratio in which 2x + 3y + 5z = 1 divides the line joining the points (1, 0, -3) and (1, -5, 7) is:
  1. 5 : 3
  2. 3 : 2
  3. 2 : 1
  4. 1 : 3
→
Find value of $x$ in equation $\left[\begin{array}{c}x+y+z \\ x+z \\ y+z\end{array}\right]=\left[\begin{array}{l}9 \\ 5 \\ 7\end{array}\right]$
→
If $P(A)=0.6, P(B)=0.3$ and $A$ and $B$ are two independent events, the value of $P(A \cap B)$ will be-
→
Choose the correct answer from the given four options.
A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement the probability of getting exactly one red ball is:
→
If vector $\vec{a}=2 \hat{i}+5 \hat{j}$ and $b=2 \hat{i}-\hat{j}$ then unit vector in the direction of the vector $\vec{a}+\vec{b}$ is :
→
$\cot\Big(\text{cosec}^{-1}\frac{5}{3}+\tan^{-1}\frac{2}{3}\Big)=$
  1. $\frac{6}{17}$
  2. $\frac{3}{17}$
  3. $\frac{4}{17}$
  4. $\frac{5}{17}$
→
The corner points of the feasible region determined by the system of linear constraints are $(0,0),(0,40),(20,40),(60,20),(60,0)$. The objective function is $Z=4 x+3 y$.
Compare the quantity in Column A and Column B
Column AColumn B
Maximum of Z325
→
Let $f (x)$ be a polynomial. Then the second order derivatives of $f(e^x)$ is:
→
For an objective function $Z=a x+b y$, where $a, b>0$; the corner points of the feasible region determined by a set of constraints (linear inequalities) are $(0,20),(10,10),(30,30)$ and $(0,40)$. The condition on $a$ and $b$ such that the maximum $Z$ occurs at both the points $(30,30)$ and $(0,40)$ is
→
An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other without replacement, then the probability that both drawn balls are black, is
→