If the slope of the function $f(x)=4 X_{2}-24 X+32$ is 0 at $X=3$, then it follows that $X=3$ is a
A) local maximum
B) local minimum
C) global maximum
D) saddle point

Question

Quizplus · Accepted Answer

The slope of the function is given by its derivative. The derivative of $f(x)=4x^2-24x+32$ is $f'(x)=8x-24$. Setting $f'(x)=0$ at $x=3$ gives $8(3)-24=0$. The second derivative $f''(x)=8$ is positive, indicating a local minimum at $x=3$.

If the Slope of the Function f(x)=4X2−24X+32f(x)=4 X_{2}-24 X+32f(x)=4X2​−24X+32 Is 0 At

If the Slope of the Function $f(x)=4 X_{2}-24 X+32$ Is 0 At