anonymous
  • anonymous
determine the values of constant real numbers a and b, so that this function is differentiable at x= -5 f(x) = (ax^2) - 4x -76 x<=(-5) = bx - 1 x > 5
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[ax^2 - 4x - 76, x \le -5\] \[bx -1, x > -5\]
anonymous
  • anonymous
answers are a = -3 b = 26
anonymous
  • anonymous
what do i do to get the answers though

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zepdrix
  • zepdrix
Hmm are you sure it's -76? Or is it suppose to be 75? I get a=-3 if its a 75.. hmm Sec ill check my work, then I can hopefully explain how i got there.
anonymous
  • anonymous
yes it is -76
zepdrix
  • zepdrix
|dw:1349558391356:dw| Here is a little example. In order for this piece-wise function be continuous, the limit from the left, needs to EQUAL, the limit from the right (approaching -5). That's why I drew those little arrows, to show that we're approaching -5 from each side. Also, their tangent line's need to be approaching the same value at that point -5. Meaning, their derivatives must be equal when approaching from the left and right. So we have a little bit of work to do. And it will give us a system of 2 equations, and we'll be able to solve for a and b from there.
anonymous
  • anonymous
oh ok
anonymous
  • anonymous
do we differentiate each equation
zepdrix
  • zepdrix
|dw:1349558662733:dw|
zepdrix
  • zepdrix
Oh i see where I made a mistake in my notes :) ok ok good this will work out fine I think.
zepdrix
  • zepdrix
|dw:1349558827441:dw| the -20 should be a +20 in the first picture i did.
zepdrix
  • zepdrix
|dw:1349558961847:dw| And from here, you have a system of equations and should be able to solve for a and b!! :) If you're stuck on how to solve the system, you can let me know.
anonymous
  • anonymous
so we have a choice of what equations wewant to use to solve for a and b?
zepdrix
  • zepdrix
Mmmm no i think we have to use both of them :)
anonymous
  • anonymous
oh ok
zepdrix
  • zepdrix
|dw:1349559254725:dw|
anonymous
  • anonymous
hey , i got it, thanks!
zepdrix
  • zepdrix
Yayyy iop \:D/
anonymous
  • anonymous
:D thnks for helping

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