Let k and m be positive real numbers such that the function f(x)=\ cc3 x²+k √(x+1), 0 0. Then (8 f^()(8))/(f^()(1/8)) is equal to _ _ _ _ _ _.

Limit, Continuity and Differentiability: JEE Main 2023 Mathematics question

JEE Main 2023 · 8 Apr, Evening shift · Q36

JEE Main 20238 Apr, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let

\mathrm{k}

and

\mathrm{m}

be positive real numbers such that the function

f(x)=\left\{\begin{array}{cc}3 x^{2}+k \sqrt{x+1}, & 0 < x < 1 \\ m x^{2}+k^{2}, & x \geq 1\end{array}\right.

is differentiable for all

x > 0

. Then

\frac{8 f^{\prime}(8)}{f^{\prime}\left(\frac{1}{8}\right)}

is equal to ____________.

Your answerType your answer. Integers and decimals are accepted.