If the equation of the tangent line is y = mx + c we have
So we want to find distinct points x=a and x=b such that
Let u = a + b and v = ab; then [3] and [4] can be expressed as
Substituting into [6]
But
We reject this since a and b must be distinct.
Hence
]]>Solution
]]>yes they are on the curve
]]>f(x)=3x^4-4x^3
at two different points
]]>