Identify where any horizontal tangents exist for the function:

Question

𝑓(𝑥)=𝑥³+7𝑥²−8

Answer 1

Horizontal tangents will occur any place the first derivative (slope) is equal to 0, i.e.:

3x² + 14x = 0

Factor and solve for x. You should get two x-coordinates where the slope is equal to 0. You can calculate the associated y coordinates by plugging the x coordinates into the original equation.