Let k and m be positive real numbers such that the function f(x)={\\begin{array}{c}3 x^2+k \sqrt{x+1\end{array}, 0 < x < 1 ; m x^2+k^2, x \geq 1\}} is differentiable for all x>0. Then {8 f^{'}(8)}/{f^{'} (\frac{1}{8}) } is equal to ________. [8-Apr-2023 shift 2]

JEE Mains 8-Apr-2023 Shift 2 Solved Paper

Section: Mathematics

Question : 30 of 90

Marks: +1, -0

Let k and m be positive real numbers such that the function f(x)={

3x2+k√x+1	0<x<1
mx2+k2	‌‌x≥1

} is differentiable for all x>0. Then ‌

8f′(8)

f′(‌

)

is equal to ________.

[8-Apr-2023 shift 2]

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