[tex]DERIVATIVES \\ \\ \\ We're \: given \: the \: expression \: \: - \\ \\ f(x) \: = 3x - 2 \sqrt{x} \\ \\ f'(x)= 3 - 2( \frac{1}{2 \sqrt{x} } ) \\ \\ f'(x)=3 - \frac{1}{ \sqrt{x} } \\ \\ Now \: , \: We've \: to \: find \: the \: value \: \\ of \: f'(1) \: \: f'(4 ) \: \: and \: \: f'( {a}^{2} ) \\ \\ \\ f'(1) = 3 - \frac{1}{ \sqrt{1} } = 3 - 1 = 2 \\ \\ \\ f'(4) = 3 - \frac{1}{ \sqrt{4} } = 3 - \frac{1}{2} = \frac{5}{2} \\ \\ \\ f'( {a}^{2} ) = 3 - \frac{1}{ \sqrt{ {a}^{2} } } = 3 - \frac{1}{a} = \frac{3a - 1}{a} [/tex]
