Use the price demand equation below to find \( E(p) \), the elasticity of demand. \( x=f(p)=5100-3 p^{2} \) \( E(p)=\square \)

To find the elasticity of demand \( E(p) \), we can use the formula for price elasticity of demand: \[ E(p) = \frac{f'(p) \cdot p}{f(p)} \] First, we need to find \( f'(p) \), the derivative of \( f(p) \): \[ f(p) = 5100 - 3p^2 \implies f'(p) = -6p \] Next, we substitute \( f(p) \) and \( f'(p) \) into the elasticity formula: \[ E(p) = \frac{-6p \cdot p}{5100 - 3p^2} = \frac{-6p^2}{5100 - 3p^2} \] Thus, the elasticity of demand is: \[ E(p) = \frac{-6p^2}{5100 - 3p^2} \] So, whatever value of \( p \) you plug in, you'll get the elasticity of demand \( E(p) \) calculated accordingly!