Find all the values of x for the horizontal tangent line of f(x)=12x^2+7x

Answer 1

f = 12x^2 +7x = 12(x^2 + 7x/12 + 49/144) - 49/12

vertex is (-7/24, -49/12)

tangent has slope = f' = 24x +7

y =-49/12 is the tangent line with slope = 0, tangent to the vertex

for x > -7/24, the slope >0

for x< -7/24, the slope <0