MCQ
If $f(x) = k{x^3} - 9{x^2} + 9x + 3$ is monotonically increasing in each interval, then
- A$k < 3$
- B$k \le 3$
- ✓$k > 3$
- DNone of these
✓
Answer
Correct option: C.
$k > 3$
c
(c) $f'(x) = 3k{x^2} - 18x + 9 = 3\,\,[k{x^2} - 6x + 3] > 0,\,\,\forall x \in R$
(c) $f'(x) = 3k{x^2} - 18x + 9 = 3\,\,[k{x^2} - 6x + 3] > 0,\,\,\forall x \in R$
$\therefore \Delta = {b^2} - 4ac < 0\,\,\,,k > 0$
$i.e.,\;\;36 - 12k < 0$ or $k > 3$.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If the curve $ay+x^2=7$ and $x^3=y,$ cut orthogonally at $(1, 1)$ then the value of a is:
→The magnitude of each of the two vectors $\vec{a}$ and $\vec{b}$, having the same magnitude such that the angle between them is $60^{\circ}$ and their scalar product is $\frac{9}{2}$, is
→Statement $1$ : If $A$ and $B$ be two sets having $p$ and $q$ elements respectively, where $q > p$. Then the total number of functions from set $A$ to set $B$ is $q^P$.
Statement $2$ : The total number of selections of $p$ different objects out of $q$ objects is ${}^q{C_p}$.
→Statement $2$ : The total number of selections of $p$ different objects out of $q$ objects is ${}^q{C_p}$.
Let $a, b, c$ be distinct non-negative numbers. If the vectors $ai + aj + ck,\,\,i + k$ and $ci + cj + bk$ lie in a plane, then $c$ is
→The feasible region of an LPP is given in the following figure
Then, the constraints of the LPP are $x \geq 0, y \geq 0$ and
→Then, the constraints of the LPP are $x \geq 0, y \geq 0$ and
$\int_{}^{} {\frac{1}{{1 + {{\sin }^2}x}}\;dx = } $
→If points $(1, 2), (3, 5)$ and $(0, b)$ are collinear the value of $b$ is :
→If $A = \left[ \begin{array}{l}1\\2\\3\end{array} \right],$then $AA' = $
→Choose the correct answer from the given four options.The differential equation for which $\text{y}=\text{a}\cos\text{x}+\text{b}\sin\text{x}$ is a solution, is:
→If $y = {\sin ^2}\alpha + {\cos ^2}(\alpha + \beta ) + 2\sin \alpha \sin \beta \cos (\alpha + \beta )$, then ${{{d^3}y} \over {d{\alpha ^3}}}$ is, (keeping $\beta $ as constant)
→