For what value of b is the line y=-12x+b tangent to the curve at y=2x^2

Answer 1

y=-12x + b = mx+b where m=slope and b = y-intercept

is tangent to y=2x^2 if the slopes are the same at their intersection

y' = 4x = -12 = slope

x =-12/4 =-3

y=2x^2 = 2(-3)^2 = 2(9) = 18

18=-12(-3)+ b

18=36 + b

b = 18-36 = -18

Answer 2

dy/dx=4x

and dy/dx=4x=-12 when x=-3

at x=-3, y= 18

therefore

18 = -12(-3) + b

b=-18