Find the equation of the curve described: The cubic y=ax^3 +bx^2 +cd +d that passes through the points (-1,-10) and (1,-4), and tangent to the line 2x+y+7=0 at (0,-7)

Question

Find the equation of the curve described:        The cubic y=ax^3 +bx^2 +cd +d that passes through the points (-1,-10) and (1,-4), and tangent to the line 2x+y+7=0 at (0,-7)

anonymous · Answer

what do you think?

aum · Answer

y = ax^3 + bx^2 + cx + d  ---- (1)
You have 4 unknowns: a, b, c and d.  
So you will need 4 equations to solve for them.

You are given three points on the curve: (-1,-10),  (1,-4),  (0,-7)
Substitute the x and y values into (1) and you will get 3 equations.

Find the slope of the tangent to the curve at (0, -7) by finding the derivative y' and substituting x = 0.  Equate it to the slope of the line 2x + y + 7 = 0.  This will be the 4th equation.  Four equations and four unknowns and you can solve for a, b, c and d.