Chapter 4 - Applications of the Derivative - 4.5 Linear Approximation and Differentials - 4.5 Exercises - Page 289: 47

$$dy = \left( {9{x^2} - 4} \right)dx$$

$$\eqalign{ & f\left( x \right) = 3{x^3} - 4x \cr & {\text{Differentiate }} \cr & f'\left( x \right) = \frac{d}{{dx}}\left[ {3{x^3} - 4x} \right] \cr & f'\left( x \right) = 9{x^2} - 4 \cr & {\text{Write in the form }}dy = f'\left( x \right)dx \cr & dy = \left( {9{x^2} - 4} \right)dx \cr} $$