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iop360
 2 years 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
iop360
 2 years 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

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iop360
 2 years ago
Best ResponseYou've already chosen the best response.0\[ax^2  4x  76, x \le 5\] \[bx 1, x > 5\]

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0answers are a = 3 b = 26

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0what do i do to get the answers though

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1Hmm 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.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1dw: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.

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0do we differentiate each equation

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

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1349558827441:dw the 20 should be a +20 in the first picture i did.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1dw: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.

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0so we have a choice of what equations wewant to use to solve for a and b?

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1Mmmm no i think we have to use both of them :)
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