Question

Find the derivative of f(x)=|x^2-3x+2|

Answer 1

\[f(x)=|x^2-3x+2|=\sqrt{(x^2-3x+2)^2}\]Then, differentiate it.

Answer 2

The thing that I was confused about was the fact that it's absolute value...so I have to make it piecewised...How do I figure out the piecewise derivative?

Answer 3

Nope, you don't have to..
Make use of the fact that \(|a| = \sqrt{a^2} \) and then use chain rule, you can do it.

Answer 4

See this:
http://www.analyzemath.com/calculus/Differentiation/absolute_value.html

Answer 5

Ok, but the answer that the professor wants from me is a piecewise function.

Answer 6

With all the domains. Sorry.

Answer 7

Hmm..
Then...
Do you know when the function will be positive and negative?

Answer 8

What do you mean?

Answer 9

For example, when x =3, x^2-3x+2 = 9-9+2 = 2 => Positive
Oh.. for the ''function'', I mean for x^2 - 3x +2

Answer 10

ok so will the function be positive for x>1?

Answer 11

and positive for x>2

Answer 12

and negative for 1<x<2

Answer 13

What about when x is negative?

Answer 14

what do you mean?

Answer 15

When x is negative, is f(x) positive or negative?

Answer 16

Oh i figured it out! Thank you!

Answer 17

wait, so since the function is positive when x>2 or x<1, that means that for those 2 parts, the derivative will be 2x-3 and since the function is negative from 1<x<2, the derivative will be -2x+3. Right?

Answer 18

Yes.

Answer 19

i think, @anneflys want to find derivative and domain of derivative, right ?

Answer 20

I already knew how to find the domain though.

Answer 21

how do u get domain of derivative, if derivative not ready :)

Answer 22

I figured it out. It's all good. Thanks.

Answer 23

what's derivative of f(x) did u get

Answer 24

show to me if u have cleared it, @anneflys

Answer 25

It's already up there. "wait, so since the function is positive when x>2 or x<1, that means that for those 2 parts, the derivative will be 2x-3 and since the function is negative from 1<x<2, the derivative will be -2x+3. Right?"

Answer 26

domain for 2x-3 is x>2 or x<1 and domain for -2x+3 is 1<x<2...

Answer 27

abs function always be a positive for x real numbers, so dont think that

Answer 28

The range of abs function is positive, but the domain can be negative.

Answer 29

dont u look in the sqrt have square sign (.......)^2, what's mean this

Answer 30

When x =-100
\[\sqrt{a^2} = \sqrt{(-100)^2} = |100|\]
-100 can be an input of the function..

Answer 31

|100| = 100

Answer 32

|-100| = 100

Answer 33

that's i meant :)

Answer 34

But then it's the range that must be positive, at least \(\ge\)0
But not the domain!

Answer 35

Domain is the value of x (the input value), range is the output value..

Answer 36

i know, so it means range of f(x) satisfied for domain all x's real
in other word, domain = x real numbers

Answer 37

But I think the domain she needs is the domain for the corresponding piecewise function..

Answer 38

question from me for u @RolyPoly
can u determine what's the value of "x", to get f(x) not real ??

Answer 39

Do you mean for the domain, she needs to write it like this: t <1 , 1<t<2, t>2 , where \(t\in \mathbb{R} \)?

Answer 40

i just want do contradiction, to prove it

Answer 41

Hmm.. wait..
t <1 , 1<t<2, t>2
^ That doesn't include 1 and 2 :O