Hey everyone,

I recently decided to reopen to old uni maths book and work it through from cover to cover, completing every single problem, proof etc. It is taking a while, but enjoying it. I am sure I will get stuck again after this at some point, so thanks in advance everyone! Actually supposed to be working right now, but spending an hour every morning on this stuff

Anyway stuck on the following problem (R. A. Adams, Calculus a Complete Course, 5th Edition, Ch 2, ch review prob 15 if you want to know ):

Let C be the graph of y = x^3

a) show that if a /=0 then the tangent to C at x=a also intersects C at a second point x=b

b) show that the slope of C at x=b is four times its slope at x=a

c) Can any line be tangent to C at more than one point

d) Can any line be tangent to te graph of y = Ax^3 + Bx^2 + Cx + D

I have not gotten very far, but this is what I have at present:

y' = 3x^2

let x = a, therefore the tangent is: y=3a^2(x-a)+a^3 = 3a^2x - 2a^3

For a) I assume that C(b) means that y = b^3 for x=b

Then I get stuck...

Help please