anonymous
  • anonymous
Given that h(x)=x^2g(x) and g(3)=5 and g'(3)=7 find h'(3)
Calculus1
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anonymous
  • anonymous
Given that h(x)=x^2g(x) and g(3)=5 and g'(3)=7 find h'(3)
Calculus1
schrodinger
  • schrodinger
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anonymous
  • anonymous
You can use the product rule. h'(x) = f(x)g'(x) + g(x)f'(x) where in this problem f(x) = x²
anonymous
  • anonymous
so f(x)=x^2 and f'(x)=2x
anonymous
  • anonymous
right

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anonymous
  • anonymous
then evaluate them both at 3
anonymous
  • anonymous
what about g(x) and g'(x)?
anonymous
  • anonymous
well they're asking for h'(3), so you don't need g(x) and g'(x) since they gave you the values at 3.
anonymous
  • anonymous
so how would you use the product rule?
anonymous
  • anonymous
Above is the product rule generally. Specifically at x = 3. \[h'(3) = f(3)g'(3) + g(3)f'(3)\]
anonymous
  • anonymous
g(3) and g'(3) are given. f(3) and f'(3) are found by evaluating x² and 2x at 3 respectively
anonymous
  • anonymous
oh is it h'(3)=9*7+5*6
anonymous
  • anonymous
f(3) = 3² = 9 f'(3) = 2(3) = 6
anonymous
  • anonymous
yep exactly
anonymous
  • anonymous
so the answer is 93
anonymous
  • anonymous
thanks for your help peachpi
anonymous
  • anonymous
yes that's right. You're welcome

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