Download App

STD 12 - 9. differential equations — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 9. differential equations1 Mark
MCQ
A function $y = f(x)$ has a second order derivatives $f''(x) = 6(x - 1)$. If its graph passes through the point $(2, 1)$ and at that point the tangent to the graph is $y = 3x - 5$, then the function is
  • A
    ${(x + 1)^3}$
  • ✓
    ${(x - 1)^3}$
  • C
    ${(x + 1)^2}$
  • D
    ${(x - 1)^2}$
✓

Answer

Correct option: B.
${(x - 1)^3}$
b
(b) Given $f''(x) = 6(x - 1)$

$f'(x) = 3{(x - 1)^2} + {c_1}$…..$(i)$

But at point $(2, 1)$ the line $y = 3x - 5$ is tangent to the graph $y = f(x)$. Hence

${\left. {\frac{{dy}}{{dx}}} \right|_{x = 2}} = 3$ or $f'(2) = 3$.

Then from $(i)$ $f'(2) = 3{(2 - 1)^2} + {c_1}$

$3 = 3 + {c_1}$ ==> ${c_1} = 0$ i.e., $f'(x) = 3{(x - 1)^2}$

Given $f(2) = 1$

$f(x) = {(x - 1)^3} + {c_2}$ ==> $f(2) = 1 + {c_2}$

==> $1 = 1 + {c_2}$ ==> ${c_2} = 0$

Hence $f(x) = {(x - 1)^3}$.

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 STD 12 - 9. differential equations→STD 12 - 9. differential equations — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

A particle moves in a straight line with a velocity given by $\frac{{dx}}{{dt}} = x + 1$($x$ is the distance described). The time taken by a particle to traverse a distance of $99$ metre is
→
$R$ is a relation from $\{11, 12, 13\}$ to $\{8, 10, 12\}$ defined by $y = x - 3$. Then, $R^{-1}$ is:
→
Let $f : R \to R$ be a twice differentiable function satisfying $f(0) = f(1) = 0$ and $f'(x) = f^2(x) \forall x \in R$ then $\mathop {\lim }\limits_{x \to 2} \left( {f(x) + xf'(x) + {x^2}f^{''}(x)} \right)$ is greater than-
→
Rolle's theorem is applicable in case of $\phi(\text{x})=\text{a}^{\sin\text{x}},\text{a}>\text{a}$ in :
→
The number of points, at which the function $f ( x )$ $=|2 x+1|-3|x+2|+\left|x^{2}+x-2\right|, x \in R$ is not differentiable, is ............
→
Let $Q$ and $R$ be two points on the line $\frac{ x +1}{2}=\frac{ y +2}{3}=\frac{ z -1}{2}$ at a distance $\sqrt{26}$ from the point $P (4,2,7)$. Then the square of the area of the triangle $PQR$ is $....$
→
If $A$ satisfies the equation $\text{x}^2-5\text{x}^2+4\text{x}+\lambda=0$ then $A^{-1}$ exists if :
→
Let $F(\alpha ) = \left[ {\begin{array}{*{20}{c}}{\cos \alpha }&{ - \sin \alpha }&0\\{\sin \alpha }&{\cos \alpha }&0\\0&0&1\end{array}} \right]$, where $\alpha \in R.$ Then ${[F(\alpha )]^{ - 1}}$ is equal to
→
If A and B are two events such that $\text{P(A)}=\frac{4}{5},$ and $\text{P}(\text{A}\cap\text{B})=\frac{7}{10},$ then P(B|A) =
→
The function $f(x) = {x^3} - 3{x^2} - 24x + 5$ is an increasing function in the interval given below
→