Find a,b,c,d such as the cubic f(x)=ax^3+bx^2+cx+d satisfies the given conditions: Relative Max: (2,4), Relative Min(4,2),Inflection point (3,3)  

⚑ Flag

Vitalia -Simply use what you know about max, min and inflection points.Step 1, find the first derivative and set it equal to zero.  You know that x=2 and x=4 are critical points and will cause this equation to be true.  Plug those values of x into this first derivative equation (set equal to zero) and get two equations in your four variables (a,b,c,d).Step 2: Find the second derivative.  Set it equal to zero.  You know that x=3 satisfies this equation because that will be an inflection point.  Plug in x = 3 and you will have a third equation in four variables (a,b,c,d).Finally, you know that the max at x=2 will only be true if the second derivative at x=2 is <0.  Likewise, the min at x=4 must produce a second derivative >0.  Use this information to determine the 4th equation you need to solve 4 equations with 4 unknown variables.Hope this helps