Calculus
posted by Allison on .
For what values of x is the tangent line of the graph of
f(x)=8x3+36x2+46x−72
parallel to the line y=−2x+1.9 ? Enter the x values in order, smallest first, to 4 places of accuracy:
x1= ≤ x2=

f(x) = 8x³ + 36x² + 46x  72
f'(x) = 24x² + 72x + 46
The slope of y = 2x+1.9 is 2
So, we want to find values of x where f'(x) = 2
24x² + 72x + 46 = 2
24x^2 + 72x + 48 = 0
x^2 + 3x + 2 = 0
(x+1)(x+2)
So, x = 2.0000, 1.0000