The graph of y=ax^3+bx^2+ cuts the X-axis where at an angle of . At the point where it cuts the Y-axis, and it is parallel to the line . Find the constants

Question

The graph of y=ax^3+bx^2+cx+d cuts the X-axis where x=2 at an angle of 45 degrees. At the point where it cuts the Y-axis, y=6 and it is parallel to the line 5x+y=4 . Find the constants a, b, c and d

Answer 1

An angle of 45 degrees implies a slope of 1.

y' = 3ax² + 2bx

1 = 3a(2)² + 2b(2)

1 = 12a + 4b

 

The slope of the line 5x + y = 4 is -5

-5 = 3a(6)² + 2b(6)

-5 = 108a + 12b

 

Solve the system.