Find the coefficient of the squared term in the simplified form for the second derivative, f " (x) for f (x) = (x2 + 4x + 3) (4x3 - 6x2 + 8x + 1). Use the hyphen symbol, -, for negative values.

Question

Mathematics

Valentina Griffin

15 April, 05:14

Find the coefficient of the squared term in the simplified form for the second derivative, f " (x) for f (x) = (x2 + 4x + 3) (4x3 - 6x2 + 8x + 1). Use the hyphen symbol, -, for negative values.

+1

Answers (1)

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Ruby Harper · Answer 1

Answer

120

Explanation

f (x) = (x² + 4x + 3) (4x³ - 6x² + 8x + 1)

= (4x⁵ - 6x⁴ + 8x³ + x²) + (16x⁴ - 24x³ + 32x² + 4x) + (12x³ - 18x² + 24x + 3)

f (x) = 4x⁵ + 10x⁴ - 4x³ + 15x² + 28x + 3

f (x) ' = 20x⁴ + 40x³ - 12x² + 30x + 28

f (x) '' = 80x³ + 120x² - 24x + 30

The coefficient of squared term is 120.