Determine any points on the graph of the following function at which the tangent line is horizontal.
$$f ( x ) = x ^ { 2 } + 8 x - 8$$
A) $( 4,40 )$
B) $( 4,0 )$
C) $( - 4,0 )$
D) $( 0 , - 8 )$
E) $( - 4 , - 24 )$

Question

Quizplus · Accepted Answer

To find points where the tangent line is horizontal, we need to find where the derivative of the function equals zero. The derivative of $f(x) = x^2 + 8x - 8$ is $f'(x) = 2x + 8$. Setting this equal to zero gives $2x + 8 = 0$, which simplifies to $x = -4$. Substituting $x = -4$ back into the original function gives $f(-4) = (-4)^2 + 8(-4) - 8 = 16 - 32 - 8 = -24$. Therefore, the point at which the tangent line is horizontal is $(-4, -24)$.

Determine Any Points on the Graph of the Following Function f(x)=x2+8x−8f ( x ) = x ^ { 2 } + 8 x - 8f(x)=x2+8x−8

Determine Any Points on the Graph of the Following Function $f ( x ) = x ^ { 2 } + 8 x - 8$