Question

f(x)=2abs(x-40)
g(x)=(1/2)x+40 when x is less than 40
and 60 when x is equal or greater than40
Find the derivative of f(g(x)) at x=70 @Calculus1

Answer 1

Can i explain you the question?

Answer 2

Are they on?

Answer 3

Oh ok

Answer 4

Thanks

Answer 5

Hw do u delete

Answer 6

Click your name

Answer 7

i think i understand the questiona

Answer 8

Wait nut I gotta explain it

Answer 9

you have to find the composite function (it will be piecewise)
then take the derivative
then evaluate

Answer 10

Really g(x) was a graph and I guessed the equation

Answer 11

It was an equation of a line (1/2)x+40 until x = 40 and then at x =40 there was a corner and it became a straight line so I guessed that this was the equation

Answer 12

\[f(x) = 2|x-40| = \left\{\begin{array}{rcc}
80-2x& \text{if} & x < 40\\
2x -80 & \text{if} & x \geq 40
\end{array}
\right.
\]

Answer 13

What I am totally confused

Answer 14

I need f(g(x))

Answer 15

i am getting to that. it is complicated by the fact that you have two piecewise functions that you have to find the composition of. that is the hard part

Answer 16

Well f(x) is peicewise?

Answer 17

absolute value is called peice wise?

Answer 18

yes it is defined piecewise. for example
\[|x| = \left\{\begin{array}{rcc}
-x & \text{if} & x <0 \\
x& \text{if} & x \geq 0
\end{array}
\right.\]

Answer 19

Oh cool way of looking at it

Answer 20

that is why taking the derivative is a pain. you have to know what interval you are talking about. the function is piecewise and so is its derivativfe

Answer 21

so that explains why i broke up the original function into two parts. now we can find the composition

Answer 22

Well I don't treat an absolute value as a peicewise I think of it like this \[abs(x)=\sqrt{x ^{2}}\]

Answer 23

but now we are almost home free, because you want the derivative at x = 70, and you said
\[g(70)=60\] right?

Answer 24

If the equation has a corner then that means it is peicewise?

Answer 25

Cuz they gave me the graph and I kind of guessed that it was a peicewise function

Answer 26

well usually if you have a functions whose picture is not a smooth curve, you have to define it two different ways at least. if you want an equation that it. if you have something that looks like

Answer 27

you will not be able to write it as one equation

Answer 28

ok I will draw the function

Answer 29

ok but it doesn't matter that much because the derivative of your function will be one of two constants. it will either be 2 or -2 depending on the values of x