Ответ:

[tex]k = f'(x_{0} ) \\ f(x) = \sqrt{x} \\ f'(x) = \frac{1}{2 \sqrt{x} } \\x_{0} = \frac{1}{4} \\ f'(x_{0}) = \frac{1}{2 \times \sqrt{ \frac{1}{4} } } = \frac{1}{2 \times \frac{1}{2} } = 1 \\ k = 1 [/tex]