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anonymous

  • one year ago

How do you calculate new functions from old ones using table quantities (x, f(x), g(x), f'(x), g'(x))?

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  1. anonymous
    • one year ago
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    Do you have a specific question? It might be easier to help you with more details.

  2. anonymous
    • one year ago
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    yes there's a table that goes along with it.

  3. anonymous
    • one year ago
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    yes there's a table that goes along with it.

  4. jim_thompson5910
    • one year ago
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    @tigel__ post the screenshot of the full problem please

  5. anonymous
    • one year ago
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  6. anonymous
    • one year ago
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    The third one's the easiest by a slight margin. \[\frac{f(-2)}{g(-2)+5}=\frac{23}{13+5}\] Do you see how I got that?

  7. anonymous
    • one year ago
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    The second one could come next. Recall that \((fg)(x)=f(x)g(x)\), so \[(fg)(4)=f(4)g(4)=-97\times25\] For the other two, you'll need to take derivatives. By the product rule (for the fourth problem): \[(fg)'(-2)=f'(-2)g(-2)+f(-2)g'(-2)=-32\times13+23\times(-10)\] By the chain rule (for the first one): \[h'(4)=\bigg(g(f)\bigg)'(4)=g'(f(4))f'(4)=g'(-97)f'(4)=\cdots\] Does that make sense?

  8. anonymous
    • one year ago
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    No I'm confused. on the first one

  9. jim_thompson5910
    • one year ago
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    @tigel__ the one where you put -9700 ?

  10. anonymous
    • one year ago
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    yes

  11. jim_thompson5910
    • one year ago
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    (fg)(x) = (f*g)(x) (fg)(x) = f(x)*g(x) (fg)(4) = f(4)*g(4) (fg)(4) = -97*25 (fg)(4) = -2425

  12. jim_thompson5910
    • one year ago
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    I got f(4) and g(4) from the table look in the f(x) row and column that starts with 4 to get f(4) similar for g(4)

  13. anonymous
    • one year ago
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    Oh im sorry! I meant the other one the one above it,

  14. jim_thompson5910
    • one year ago
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    oh ok

  15. jim_thompson5910
    • one year ago
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    h(x) = g(f(x)) h ' (x) = g ' (f(x)) * f ' (x) ... chain rule h ' (4) = g ' (f(4)) * f ' (4) ... replace every x with 4 h ' (4) = g ' (-97) * f ' (4) ... use the table h ' (4) = (-390) * (-80) ... use the table h ' (4) = 31,200

  16. jim_thompson5910
    • one year ago
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    f(4) = -97 f ' (4) = -80 g ' (-97) = -390

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