Calc. question and I need help please! Thanks!

Question

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

Answer 1

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

 

Step 1: Finding the 4th degree term of f(x)

 

It is (x³)(-8x) + (3x²)(-6x²) = -26x⁴

 

Step 2: Take the second derivative of this term

 

d²/dx² (-26x⁴) = -312x²

 

So the x² term of f''(x) has coefficient -312.