Find the values of x for which y=3x^4 + 13x^3 + 18x^2 - 3x^2 + 6 is convex

Please help! A-Level Pure Maths Edexel. Here’s what I’ve done so far:
d^2y/dx^2 = 36x^2 + 78x + 36 > 0

Stuck where to go next without using calculator?

Reply 1

Jam.123

Original post

by deskio

Please help! A-Level Pure Maths Edexel. Here’s what I’ve done so far:
d^2y/dx^2 = 36x^2 + 78x + 36 > 0
Stuck where to go next without using calculator?

I think you should have a go at solving the inequality. "If it's tricky, draw a piccy..."

Reply 2

mqb2766

Original post

by deskio

Please help! A-Level Pure Maths Edexel. Here’s what I’ve done so far:
d^2y/dx^2 = 36x^2 + 78x + 36 > 0
Stuck where to go next without using calculator?

You can use a calc at a level, but the roots of the quadratic arnt that bad if you want to do it manually. So factor out or divide by 6 or 36 and the usual solve the quadratic. Then simple reasoning about the intervals.

(edited 11 months ago)

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