Project ForgeEngineering Mathematics
Calculus
GATE 2012
Easy
At x=0, the function f(x)=x³+1 has
- Aa maximum value.
- Ba minimum value.
- Ca singularity.
- a point of inflection.
Explanation
f′(x)=3x², f′(0)=0 (stationary point candidate), but f″(x)=6x, f″(0)=0 too, so the second-derivative test is inconclusive. Checking f″ around x=0: it's negative for x<0 and positive for x>0 — concavity changes sign, so x=0 is a point of inflection (with a horizontal tangent), not a max/min.
Source: GATE ME 2012 (Booklet Code A) (2012)
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