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anonymous

  • one year ago

Given that h(x)=x^2g(x) and g(3)=5 and g'(3)=7 find h'(3)

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  1. anonymous
    • one year ago
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    You can use the product rule. h'(x) = f(x)g'(x) + g(x)f'(x) where in this problem f(x) = x²

  2. anonymous
    • one year ago
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    so f(x)=x^2 and f'(x)=2x

  3. anonymous
    • one year ago
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    right

  4. anonymous
    • one year ago
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    then evaluate them both at 3

  5. anonymous
    • one year ago
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    what about g(x) and g'(x)?

  6. anonymous
    • one year ago
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    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.

  7. anonymous
    • one year ago
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    so how would you use the product rule?

  8. anonymous
    • one year ago
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    Above is the product rule generally. Specifically at x = 3. \[h'(3) = f(3)g'(3) + g(3)f'(3)\]

  9. anonymous
    • one year ago
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    g(3) and g'(3) are given. f(3) and f'(3) are found by evaluating x² and 2x at 3 respectively

  10. anonymous
    • one year ago
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    oh is it h'(3)=9*7+5*6

  11. anonymous
    • one year ago
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    f(3) = 3² = 9 f'(3) = 2(3) = 6

  12. anonymous
    • one year ago
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    yep exactly

  13. anonymous
    • one year ago
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    so the answer is 93

  14. anonymous
    • one year ago
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    thanks for your help peachpi

  15. anonymous
    • one year ago
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    yes that's right. You're welcome

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