chris215
  • chris215
please help I will fan and medal! Find the coefficient of the squared term in the simplified form for the second derivative, f "(x) for f(x) = (x^3 + 3x^2 + 3)(3x^3 − 6x^2 − 8x + 1) . Use the hyphen symbol, -, for negative values.
Mathematics
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SOLVED
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chestercat
  • chestercat
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chris215
  • chris215
i got 108?
SolomonZelman
  • SolomonZelman
I don't think so.
SolomonZelman
  • SolomonZelman
It might be a pain in the neck to expand it, but once you expand it to find the second derivative and then the coefficient of x^2 shouldn't be much trouble.

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SolomonZelman
  • SolomonZelman
Oh, you don't need to expand.
Michele_Laino
  • Michele_Laino
Hint: I got this expression for \(f(x)\): \(f(x)=3x^6+3x^5-26x^4-14x^3-15x^2-24x+3\)
anonymous
  • anonymous
f"x=90x^4+60x^3-312x^2-84x-15
anonymous
  • anonymous
That should be the answer
anonymous
  • anonymous
after taking two derivatives of what Michele Lanio got
SolomonZelman
  • SolomonZelman
You know that the second derivative of ax^4 will yield the coefficient you need. What is the ax^4 in this case? (x^3)•(-8x) + (-6x^2)•(3x^2) ______________ -8x^4-18x^4=-26x^4 g(x)=-26x^4 g''(x)=(-26•3•4)x^2
SolomonZelman
  • SolomonZelman
You can ignore the rest of the terms in the f(x), just the products of those that give x^4.

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