6.1 Calculate the value of \( d \) 62 Show that \( f(x)=-x^{3}+4 x+12 \).

To calculate the value of \( d \), it’s essential to first identify the context in which \( d \) is being used. If this pertains to a specific problem or equation, sharing that equation would clarify your request. As for showing that \( f(x) = -x^3 + 4x + 12 \), you can verify this by plugging in various values of \( x \) to check if the expression yields consistent results, or by analyzing its graph to understand its behavior and properties! Now, let’s talk about cubic functions! The function \( f(x) = -x^3 + 4x + 12 \) features a distinctive shape that can lead to fascinating insights about its properties. For instance, the negative coefficient of \( x^3 \) indicates that the function will eventually decrease indefinitely as \( x \) goes to positive or negative infinity, giving it a classic 'n' shape. Additionally, cubic functions like this one can have interesting applications in real-world modeling. Many physical phenomena, such as the motion of a projectile or the shape of a suspension bridge under tension, can often be represented by cubic equations. This reflects how mathematics beautifully intertwines with the world around us!