Question

calculus problem

Answer 1

\[\Large\rm v(x)=f(f(x))\]By the definition of the chain rule:\[\Large\rm v'(x)=f'(f(x))\cdot f'(x)\]

Answer 2

\[\Large\rm v'(1)=f'(\color{orangered}{f(1)})\cdot f'(1)\]Deal with the orange part first.\[\Large\rm f(1)=?\]

Answer 3

1?

Answer 4

and derivative of 1 is 0 and for the other part 3 is also 0 .. so f(1) = 1 f(3) = 2 ... ( from the graph) ?

Answer 5

What is f(1) from the graph?

Answer 6

2

Answer 7

@ranga

Answer 8

Yes. f(1) = 2.
Put that in: f'(f(1)) as shown by zepdrix above.

Answer 9

isnt the derivative of 2 zero?

Answer 10

You need to find f'(f(1)). That is, f'(2).
f'(2) is the slope of the graph f(x) at x = 2.
What is the slope of f(x) at x = 2?

Answer 11

the slope doesnt exist cause its a corner... right

Answer 12

Exactly!

Answer 13

okay so for v'(3) = would be f'(2) aswell so DNE aswell?

Answer 14

Yes!

Answer 15

ty!