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Let y=f(x) be a thrice differentiable fu...

Let `y=f(x)` be a thrice differentiable function in `(-5,5)` .Let the tangents to the curve `y=f(x)` at `(1,f(1))` and `(3,f(3))` make angles `pi/6` and `pi/4`,respectively with positive "x" -axis.If `27int_(1)^(3)((f'(t))^(2)+1)f''(t)dt=alpha+beta sqrt(3)` where `alpha,beta` are integers,then the value of `alpha+beta` equals

A

36

B

26

C

`-16`

D

`-14`

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JEE MAINS PREVIOUS YEAR-JEE MAIN 2024 ACTUAL PAPER-Question
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