Find all the values of x (if any) where the tangent line to the graph of the given equation is horizontal. Round your answer to two decimal places.
$y = 10 x ^ { 2 } + 11 x + 5$
A) $x = - 0.55$
B) $x = - 5.5$
C) $x = 0.55$
D) $x = 5.5$
E) $x = 0$

Question

Find all the values of x (if any) where the tangent line to the graph of the given equation is horizontal. Round your answer to two decimal places. 
$y = 10 x ^ { 2 } + 11 x + 5$ 
A) $x = - 0.55$
B) $x = - 5.5$
C) $x = 0.55$
D) $x = 5.5$
E) $x = 0$

Quizplus · Accepted Answer

To find where the tangent line is horizontal, we need to find where the derivative of the function is equal to 0. The derivative of $y = 10x^2 + 11x + 5$ is $y' = 20x + 11$. Setting this equal to 0 gives $20x + 11 = 0$, which solves to $x = -\frac{11}{20} = -0.55$.

Find All the Values of X (If Any) Where the Tangent