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
Stacey Warren - Expert brainly.com
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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.
yes it is -76
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.
the -20 should be a +20 in the first picture i did.
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?