anonymous
  • anonymous
I bet you can't solve this
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
1 Attachment
ganeshie8
  • ganeshie8
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
ganeshie8
  • ganeshie8
|dw:1439872535823:dw|

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ganeshie8
  • ganeshie8
see if you can get another equation using the second condition
anonymous
  • anonymous
im sorry i dont follow D:, do you mean to plug x = 2 into x^-cx ?
ganeshie8
  • ganeshie8
I did that already and got the first equation we need another equation so that we will be able to solve the system
anonymous
  • anonymous
pick any number above 2
anonymous
  • anonymous
....for the sake of convenience pick an integer
ganeshie8
  • ganeshie8
find the derivative of left side and right side expressions : |dw:1439872985409:dw|
anonymous
  • anonymous
okay so c(4) + d = 16 - c(4) ?
ganeshie8
  • ganeshie8
whats the derivative of \(cx+d\) ?
anonymous
  • anonymous
c
ganeshie8
  • ganeshie8
good, save that whats the derivative of \(x^2-cx\) ?
anonymous
  • anonymous
2x - c
ganeshie8
  • ganeshie8
Yes, evaluate that at \(x=2\)
anonymous
  • anonymous
4 - c
ganeshie8
  • ganeshie8
set that equal to the derivative of left side expression and solve \(c\) : \[c = 4-c\]
ganeshie8
  • ganeshie8
solve \(c\)
anonymous
  • anonymous
c = 2
ganeshie8
  • ganeshie8
Yes, plug that in the first equation and solve \(d\) too
ganeshie8
  • ganeshie8
|dw:1439873439636:dw|