[tex]1)f(x) = x {}^{3} - 3x \\ \frac{d}{dx} (x {}^{3} - 3x) = 3x {}^{2} - 3 \\ \frac{d}{dx} ( - 3) = 3 \times ( - 3) {}^{2} - 3 = 24 \\ \frac{d}{dx} ( \frac{1}{2} ) = ( \frac{1}{2} ) {}^{2} \times 3 - 3 = - 2 \frac{1}{4} \\ 2)f(x) = x - 4 \sqrt{x} \\ \frac{d}{dx} (x - 4 \sqrt{x} ) = 1 - 2 \times \frac{1}{ \sqrt{x} } = 1 - \frac{2}{ \sqrt{x} } \\ \frac{d}{dx} (1) = 1 - \frac{2}{ \sqrt{1} } = - 1 \\ \frac{d}{dx} (4) = 1 - \frac{2}{ \sqrt{4} } = 0 \\ \frac{d}{dx} (0.01) = 1 - \frac{2}{ \sqrt{0.01} } = - 19[/tex]