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anonymous

  • one year ago

A. Find the derivative of f at x. That is, find f'(x). B. Find the slope of the tangent line to the graph of f at each of the two values of x given to the right of the function f(x)=x^2-8; x=-1, x=3

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  1. anonymous
    • one year ago
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    @ganeshie8

  2. misty1212
    • one year ago
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    HI!!

  3. anonymous
    • one year ago
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    Hey

  4. misty1212
    • one year ago
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    you know the derivative of \(x^2\)?

  5. misty1212
    • one year ago
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    if the answer is "no" that is fine, i will tell you

  6. anonymous
    • one year ago
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    is it 2x?

  7. misty1212
    • one year ago
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    yes

  8. misty1212
    • one year ago
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    and the derivative of a constant is zero, making the derivative of \(f(x)=x^2-8\) the function \[f'(x)=2x\] that is all

  9. anonymous
    • one year ago
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    but its two parts to the question is 2x the answer to them both

  10. anonymous
    • one year ago
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    @misty1212

  11. misty1212
    • one year ago
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    no \(2x\) is the derivative you now need the equation for two lines, one where \(x=-1\) and the other where \(x=-3\)

  12. anonymous
    • one year ago
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    f(x)=-1^2-8 and f(x)=-3^2-8

  13. misty1212
    • one year ago
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    if \(x=-1\) then \(y=(-1)^2-8=-7\) so the point is \((-1,-7)\) and the slope is \(2\times -1=-2\) use the point slope formula to get the equation of the line

  14. misty1212
    • one year ago
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    if \(x=3\) then \(y=3^2-8=1\) the point is \((3,1)\) and the slope is \(2\times 3=6\) points slope again

  15. anonymous
    • one year ago
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    y-(-7)=-2(x-(-1)) and y-(1)=6(x-(3))

  16. anonymous
    • one year ago
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    @misty1212

  17. misty1212
    • one year ago
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    you can clean them up a great deal, but yes

  18. anonymous
    • one year ago
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    y=-2x+5 y=6x-17

  19. anonymous
    • one year ago
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    @misty1212

  20. anonymous
    • one year ago
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    o Thank you

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