[tex] y_{k} = f( x_{0}) + f '( x_{0})(x - x_{0}) \\ f '(x) = (2 \sqrt{x} + {x}^{2}) ' = (2 \sqrt{x}) ' + ( {x}^{2}) ' = \\ = (2' \times {x}^{ \frac{1}{2} } + 2 \times ({x}^{ \frac{1}{2} })') + 2x = {x}^{ - \frac{1}{2} } + 2x \\ y_{k} = (2 \times \sqrt{1} + {1}^{2}) + ( {1}^{ - \frac{1}{2} } + 2 \times 1)(x - 1) = 3 + 3(x - 1) = \\ = 3 + 3x - 3 = 3x[/tex]