Find a cubic function
y = ax3 + bx2 + cx + d whose graph has horizontal tangents at the points (-2,12) and (2,6)

Question

Find a cubic function 
y = ax3 + bx2 + cx + d whose graph has horizontal tangents at the points (-2,12) and (2,6)

aum · Answer

You have four unknowns: a, b, c and d  and therefore you will need 4 equations to solve for them.  You are already given two points ON the curve:  (-2, 12) and (2,6).  Plug the numbers into the function and you have two equations.  Then, ...

aum · Answer

To find the slope, take the derivative of the function.  "Horizontal tangent" means the slope at those points are zero.  Plug the x values of -2 and 2 and set the corresponding y' to zero and you will have two more equations.  Solve the 4 simultaneous equations to find a, b, c and d.