Aspire's Library
A Place for Latest Exam wise Questions, Videos, Previous Year Papers,
Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Let \( \alpha, \beta \in \mathbb{R} \) be such that the function
\(
f(x)=
\begin{cases}
2\alpha(x^2-2)+2\beta x, & x<1 \\
(\alpha+3)x+(\alpha-\beta), & x\ge 1
\end{cases}
\)
be differentiable at all \( x\in\mathbb{R} \). Then \( 34(\alpha+\beta) \) is equal to:
Solution
Continuity at $x=1$
$2\alpha(1-2)+2\beta = (\alpha+3)+(\alpha-\beta)$
$-2\alpha+2\beta = 2\alpha-\beta+3$
$\Rightarrow 4\alpha-3\beta+3=0$ …(1)
Differentiability
$f'(x<1)=4\alpha x+2\beta \Rightarrow f'(1)=4\alpha+2\beta$
$f'(x\ge1)=\alpha+3$
$4\alpha+2\beta=\alpha+3$
$\Rightarrow 3\alpha+2\beta-3=0$ …(2)
Solving (1) & (2)
$\alpha=\frac{3}{17},; \beta=\frac{21}{17}$
$34(\alpha+\beta)=34\cdot\frac{24}{17}=48$
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
Ask Your Question or Put Your Review.
