Line L is tangent to y=5x^2+8x and parallel to 12x+y=4. What is the y-intercept of line L?

Question

AP Calculus AB

Answer 1

y = 5x^2 +8x ----------------(1)

So, tangent to the curve is y' = 10x +8

Also, the slope of the tangent to the curve that is parallel to 12x+y=4 or y=-12x+4 is -12

Therefore,

10x + 8 = -12 

or 10x =-20

or x=-2

putting the value of x in (1) we get:

y = 5(4) +8(-2) = 4

So the equation of L is y-4=-12(x+2)

or y = -12x -24 +4

or y = -12x -20

So the y intercept of line L is -20