lean_workbook_plus_70365

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

Find the value of $mb^2$ for the line tangent to the graph of $y = \sqrt [3]{x}$ at $x = 2008^3 + 2008 + 1$ in the form $y = mx + b$ without using calculus.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_70365 (m b x : ℝ) (hx: x = 2008^3 + 2008 + 1) (hb: b = 2008^2 + 2008) (hm: m = 1 / (3 * 2008^2/3)):  m * b^2 = 4/27   :=  by sorry

The slope/intercept are inserted numerals unrelated to the tangent condition, and the slope formula is malformed.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

For any a>0, let r=∛a and consider the tangent to y=∛x at(a,r). Prove its slope m=1/(3r²), intercept b=2r/3, and mb²=4/27; specialize a=2008³+2008+1. Define tangency geometrically or by a derivative rather than assuming incorrect m,b.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.