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anonymous

  • one year ago

I bet you can't solve this

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  1. anonymous
    • one year ago
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  2. ganeshie8
    • one year ago
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    If \(f(x)\) is differentiable at \(x=2\), then it must satisfy below two conditions : 1) \(f(x)\) must be continuous at \(x=2\) 2) slope of tangent lines from left and right sides must be equal

  3. ganeshie8
    • one year ago
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    |dw:1439872535823:dw|

  4. ganeshie8
    • one year ago
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    see if you can get another equation using the second condition

  5. anonymous
    • one year ago
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    im sorry i dont follow D:, do you mean to plug x = 2 into x^-cx ?

  6. ganeshie8
    • one year ago
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    I did that already and got the first equation we need another equation so that we will be able to solve the system

  7. anonymous
    • one year ago
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    pick any number above 2

  8. anonymous
    • one year ago
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    ....for the sake of convenience pick an integer

  9. ganeshie8
    • one year ago
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    find the derivative of left side and right side expressions : |dw:1439872985409:dw|

  10. anonymous
    • one year ago
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    okay so c(4) + d = 16 - c(4) ?

  11. ganeshie8
    • one year ago
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    whats the derivative of \(cx+d\) ?

  12. anonymous
    • one year ago
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    c

  13. ganeshie8
    • one year ago
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    good, save that whats the derivative of \(x^2-cx\) ?

  14. anonymous
    • one year ago
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    2x - c

  15. ganeshie8
    • one year ago
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    Yes, evaluate that at \(x=2\)

  16. anonymous
    • one year ago
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    4 - c

  17. ganeshie8
    • one year ago
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    set that equal to the derivative of left side expression and solve \(c\) : \[c = 4-c\]

  18. ganeshie8
    • one year ago
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    solve \(c\)

  19. anonymous
    • one year ago
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    c = 2

  20. ganeshie8
    • one year ago
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    Yes, plug that in the first equation and solve \(d\) too

  21. ganeshie8
    • one year ago
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    |dw:1439873439636:dw|