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Limits Continuity and Differentiability question

2023 · 8 Apr · Shift 2 · Q39

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PYQ Library
JEE Main
Mathematics
Limits Continuity and Differentiability
2023 · 8 Apr · Shift 2 · Q39

Limits Continuity and Differentiability question

2023 · 8 Apr · Shift 2 · Q39

JEE MainMathematicsLimits Continuity and DifferentiabilityNumerical+4 / −1

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 \lt x \lt 1 \\ m x^{2}+k^{2}, & x \geq 1\end{array}\right.

is differentiable for all

x \gt 0

. Then

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

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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