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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
 one year ago
 one year ago
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
 one year ago
 one year ago

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iop360Best ResponseYou've already chosen the best response.0
\[ax^2  4x  76, x \le 5\] \[bx 1, x > 5\]
 one year ago

iop360Best ResponseYou've already chosen the best response.0
answers are a = 3 b = 26
 one year ago

iop360Best ResponseYou've already chosen the best response.0
what do i do to get the answers though
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
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.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
dw:1349558391356:dw Here is a little example. In order for this piecewise 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.
 one year ago

iop360Best ResponseYou've already chosen the best response.0
do we differentiate each equation
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Oh i see where I made a mistake in my notes :) ok ok good this will work out fine I think.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
dw:1349558827441:dw the 20 should be a +20 in the first picture i did.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
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.
 one year ago

iop360Best ResponseYou've already chosen the best response.0
so we have a choice of what equations wewant to use to solve for a and b?
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Mmmm no i think we have to use both of them :)
 one year ago

iop360Best ResponseYou've already chosen the best response.0
hey , i got it, thanks!
 one year ago
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