The line y=x+4 is tangent to y=x³+3x²+x at A. Find A.

01 / Standard#Your turn

Official paper · jm02-2023 · 2(b)(i) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Match the derivative to the line slope 1.

Hint 2

A candidate must also lie on the given line.

Worked solution

Find the possible tangent abscissae.
$3x^2+6x+1=1\implies x=0,-2$
Check the curve values against the line.
$x=0:\ 0\ne4;\quad x=-2:\ -8+12-2=2=-2+4$

A=(−2,2).

Checks and common pitfalls: Equal slopes alone do not guarantee tangency to this particular line.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Find the possible tangent abscissae.
$3x^2+6x+1=1\implies x=0,-2$
Check the curve values against the line.
$x=0:\ 0\ne4;\quad x=-2:\ -8+12-2=2=-2+4$

Think first. Reveal a hint when the class is ready.

2023 JM02