Download App

Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
The function $f(x)=x^3-3 x^2+12 x-18$ is :
  • A
    strictly decreasing on $R$
  • B
    strictly increasing on $R$
  • C
    neither strictly increasing nor strictly decreasing on $R$
  • D
    strictly decreasing on $(-\infty, 0)$
✓

Answer

$\begin{array}{l}\text {} f(x)=x^3-3 x^2+12 x-18 \\ \Rightarrow \quad f^{\prime}(x)=3 x^2-6 x+12=3\left(x^2-2 x+1^2\right)+9 \\ =3(x-1)^2+3^2>0 \forall x \in R \\ \Rightarrow \quad f(x) \text { is strictly increasing on } R\end{array}$

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→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Using the factor theorem it is found that a + b, b + c and c + a are three factors of the determinant $\begin{vmatrix}-2\text{a}&\text{a}+\text{b}&\text{a}+\text{c}\\\text{b}+\text{a}&-2\text{b}&\text{b}+\text{c}\\\text{c}+\text{a}&\text{c}+\text{b}&-2\text{c}\end{vmatrix}$ the other factor in the value of the determinant is:
  1. 4
  2. 2
  3. a + b + c
  4. None of these.
→
The maximum value of $Z=3 x+4 y$ subject to the constraints $x \geq 0, y \geq 0$ and $x+y \leq 1$ is
→
The ordinate of a point describing the circle $x^2 + y^2 = 25$ decreases at the rate of $1\, cm/sec$, then the rate of change of abscissa of the point when ordinate equal to $3\,cm$ is- (Given $x > 0, y > 0$)
→
If $ 5$  is one root of the equation $\left| {\,\begin{array}{*{20}{c}}x&3&7\\2&x&{ - 2}\\7&8&x\end{array}\,} \right| = 0$, then other two roots of the equation are
→
$\int_{}^{} {\frac{{dx}}{{1 + {e^x}}} = } $
→
An operation * is defined on the set Z of non-zero integers by a * b = ab for all a, b ∈ Z. Then the property satisfied is:
  1. Closure.
  2. Commutative.
  3. Associative.
  4. None of these.
→
If $\left|\begin{array}{ccc}5 & 3 & -1 \\ -7 & x & -3 \\ 9 & 6 & -2\end{array}\right|=0$, then the value of $x$ is
→
The general solution of the differntial equation $\frac{\text{dy}}{\text{dx}}+\text{y}\cot\text{x}=\text{coses}\ \text{x}$ is: 
  1. $\text{x}+\text{y}\sin\text{x}=\text{C}$
  2. $\text{x}+\text{y}\cos\text{x}=\text{C}$
  3. $\text{y}+\text{x}(\sin\text{x}+\cos\text{x})=\text{C}$
  4. $\text{y}\sin\text{x}=\text{x}+\text{C}$ 
→
If $ \displaystyle \begin{vmatrix} 2 &\text{amp;} -4 \\ 9 &\text{amp; d}-3 \end{vmatrix}=4$ then $\text{d}=$
  1. 10
  2. −11
  3. 12
  4. −13
→
Solution of the equation $\left| {\,\begin{array}{*{20}{c}}1&1&x\\{p + 1}&{p + 1}&{p + x}\\3&{x + 1}&{x + 2}\end{array}\,} \right| = 0$ are
→