Evaluate \( p''(1) \):
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- p'(1) = 4 imes 1^3 - 12 imes 1^2 + 12 imes 1 - 4 = 4 - 12 + 12 - 4 = 0
- 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
- p''(1) = 12 imes 1^2 - 24 imes 1 + 12 = 12 - 24 + 12 = 0
- Compute the third derivative \( p'''(x) \):
- p'''(x) = 24x - 24
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