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Limits Continuity and Differentiability question

2025 · 22 Jan · Shift 1 · Q45

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JEE Main
Mathematics
Limits Continuity and Differentiability
2025 · 22 Jan · Shift 1 · Q45

Limits Continuity and Differentiability question

2025 · 22 Jan · Shift 1 · Q45

JEE MainMathematicsLimits Continuity and DifferentiabilityNumerical+4 / −1

Let the function,

f(x)= \begin{cases}-3 \mathrm{ax}^2-2, & x\lt 1 \\ \mathrm{a}^2+\mathrm{b} x, & x \geqslant 1\end{cases}

be differentiable for all

x \in \mathbf{R}

, where

\mathrm{a}\gt 1, \mathrm{~b} \in \mathbf{R}

. If the area of the region enclosed by

y=f(x)

and the line

y=-20

is

\alpha+\beta \sqrt{3}, \alpha, \beta \in Z

, then the value of

\alpha+\beta

is

\underline{\hspace{2cm}}

.

Numerical answer

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