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onegirl

Find an equation of the tangent line to h(x) = f(x)g(x) at x = 1

  • one year ago
  • one year ago

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  1. ingenuus
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    \[y=[f'(1)g(1) + f(1)g'(1)](x-1) + f(1)g(1)\]

    • one year ago
  2. campbell_st
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    well you need the point of the curve which will be (1, h(1)) you need to find the slope... but 1st you need to differentiate the function using the product rule h'(x) = f(x)g'(x) + g(x)f'(x) the slope at x = 1 is found by substituting x = 1 into the 1st derivative(above) h'(1) = f(1)g'(1) + g(1)f'(1) now you have a slope h'(1) and point (1, h(1)) use the point slope formula to find the equation of the tangent.

    • one year ago
  3. onegirl
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    ok

    • one year ago
  4. onegirl
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    so i got y = g(1)f'(1) + f(1)x g'(1) - f(1) g'(1) + f(1)g(1) is it correct?

    • one year ago
  5. onegirl
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    @campell_st ?

    • one year ago
  6. onegirl
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    @campbell_st

    • one year ago
  7. onegirl
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    @ingenuus did i get it right?

    • one year ago
  8. ingenuus
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    no the answer is above

    • one year ago
  9. onegirl
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    okay

    • one year ago
  10. ingenuus
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    do you understand the equation y=m(x-a) +b ?

    • one year ago
  11. onegirl
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    yes

    • one year ago
  12. ingenuus
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    what is the slope m in your case

    • one year ago
  13. onegirl
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    1?

    • one year ago
  14. ingenuus
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    why is it 1?

    • one year ago
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