Here's the question you clicked on:
iop360
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
\[ax^2 - 4x - 76, x \le -5\] \[bx -1, x > -5\]
answers are a = -3 b = 26
what do i do to get the answers though
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.
|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.
do we differentiate each equation
Oh i see where I made a mistake in my notes :) ok ok good this will work out fine I think.
|dw:1349558827441:dw| the -20 should be a +20 in the first picture i did.
|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.
so we have a choice of what equations wewant to use to solve for a and b?
Mmmm no i think we have to use both of them :)