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Home / p''(1) = 12 imes 1^2 - 24 imes 1 + 12 = 12 - 24 + 12 = 0

p''(1) = 12 imes 1^2 - 24 imes 1 + 12 = 12 - 24 + 12 = 0

February 22, 2026

p''(1) = 12 imes 1^2 - 24 imes 1 + 12 = 12 - 24 + 12 = 0

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Since \( p'(1) = 0 \), \( x = 1 \) is a root of multiplicity at least 2. Compute the second derivative \( p''(x) \):
p''(x) = 12x^2 - 24x + 12
Evaluate \( p''(1) \):
Compute the third derivative \( p'''(x) \):
p'''(x) = 24x - 24
p'''(1) = 24 imes 1 - 24 = 0

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