Question

the function (f(x)=-x^{2}-13x - 42) has a maximum at the point

Explanation:

Step1: Find the derivative

The derivative of $f(x)=-x^{2}-13x - 42$ using the power - rule $(x^n)'=nx^{n - 1}$ is $f'(x)=-2x-13$.

Step2: Set the derivative equal to zero

Set $f'(x) = 0$, so $-2x-13 = 0$. Solving for $x$ gives $-2x=13$, then $x=-\frac{13}{2}$.

Step3: Check the second - derivative

The second - derivative $f''(x)=-2<0$. Since $f''(x)<0$, the function has a maximum at $x =-\frac{13}{2}$.

Answer:

$x =-\frac{13}{2}$