HL maths paper 1 help please.

cocopopsxx

Hey, I can't figure out how to do two questions, 1 algebra and 1 differentiation so I was wondering if someone could help. Here they are-

-Differentuation question:

Y=ax^2+bx+c. The curve passes through (2,4) and Y=x+1 is tangent at (0,1). find a,b,c €R

-Algebra question:

p,q and r are positive numbers such that no two numbers are equal

(i) show that p^3 + q^3 > pq(p+q)

(ii) hence, or otherwise, show that

2(p^3 + q^3 + r^3) > p^2(q+r) + q^2 (p+r) + r^2(p+q)

I could do part (i) alright but can't do part (ii)

Help please x

MathsManiac

First one:

The fact that it passes through (2, 4) gives you one equation in a, b, and c.
The fact that it passes through (0, 1) gives you another equation in a, b, and c. (Tells you what c is, in fact).
The fact that the tangent at (0, 1) has slope 1 tells you that dy/dx = 1 when x = 0. (Tells you what b is, in fact).

You should be able to finish from there.

cocopopsxx

Thank you MathsManiac

finality

This is the algebra question. Basically you have to get the second part into 3 pieces that are the same as part (i), then say they're all greater than 0 separately so they must be greater than 0 when added. I didn't know how to explain that very well so it's probably clearer to see it done out.

cocopopsxx

Thank you finality. That makes sense finally!

Cheers lads!