The curve y=(ax+b)^2(c-x) cuts the x-axis at 3 and touches the x axis at x=9/4. Find the values of a,b,c.
If it "touches" the x axis at x=9/4, it means that the x axis is tangent to the curve at this point.
This means two things :
- the derivative at this point is 0.
- the point (9/4,0) is a point on a curve.
Now, substitute all this information in the equation. It should give you 3 equations with 3 unknowns.
Could you also take advantage of the fact that where it "touches" the x axis the power of the bracket must be even?
Since it cuts the x axis the power of the bracket must be odd (in this case 1):
I haven't worked through the rest of it yet but will this way work as well?
(you would need to find another equation linking and c and b or c and a. Differentiation can be used for this).