4-1-43
X
00:00
/
00:00
CC
Using the product role, we get F prime of X equaling the
derivative of the first which is one times the second plus the
derivative of the 2nd.
So we bring down the three.
We take the 16 -, X to the one less power and then we have to
do the chain role, so the derivative of the inside -1
times the first term of the X.
So we have 16 -, X squared in common between those two terms.
So we're going to factor out a 16 -, X From there.
We get left a 16 - X - 3 X or 16 - 4 X.
If I pull out a four from that last parenthesis, I get four
times the quantity 16 - X ^2 times the quantity 4 - X.
If I think about putting that on a number line, we have our four
and we have our 16 from our two parentheses.
If I put a number pass 16 to the right, 17/18/19 a million, I'm
going to get a negative value because that 16 -, X ^2 will
turn positive, but 4 minus something big is going to be a
negative at 16.
That's going to keep being a negative on the other side
because of the quantity squared.
That multiplicity at 4:00, it's going to change from a negative
to a positive because it's multiplicity is 1.
So we know that from negative Infinity to four, the original
function will be increasing, from 4 to 16 the original
functions decreasing, and from 16 to Infinity the original
functions decreasing.
So critical points here are going to be 4 and 16.