Answer: The required value of the derivative is -135.
Step-by-step explanation: We are given to find the derivative of the function f(x) defined as follows :
\(f(x)=-12x^2+9x~~\textup{at }x=6.\)
We have
\(f(x)=-12x^2+9x.\)
Differentiating both sides with respect to x, we have
\(\dfrac{d}{dx}f(x)=\dfrac{d}{dx}(-12x^2+9x)=-12\times2x+9=-24x+9.\)
Therefore, at x = 6, we get
\(\dfrac{d}{dx}f(x)=-24\times6+9=-144+9=-135.\)
Thus, the required value of the derivative is -135.
