Question

help ASAP calculus question

Answer 1

If h(x) = f[f(x)] use the table of values for f and f ′ to find the value of h ′(1).

TABLE:

x f(x) f'(x)
1 3 2
2 1 5
3 6 7

Answer 2

@steve816

Answer 3

someone please

Answer 4

???

Answer 5

@AMQ *cough cough*

Answer 6

and you think i know calculus?

Answer 7

@Bob ??? x'D

Answer 8

thanks for the complement though ;)

Answer 9

use the chain rule

Answer 10

\[h'(x)=f'(f(x))f'(x)\]

then evaluate at \(x=1\)

Answer 11

From the table, obtain the values of the following: f(1), f'(1), f'(3). Give this a try.

Answer 12

@zarkon can you explain further please

Answer 13

i seriously need help lmao

Answer 14

@wo1f0mon

Answer 15

umm i know how add and subtract

Answer 16

so i dont know how do dis sorry!

Answer 17

Simply stated, you have to use the Chain Rule.

Supposing that f(x) and g(x) are functions, h(x) = f ( g(x) ) is called a "composite function." The Chain Rule pertains to differentiating such a function.

Here is the formula for this situation:

h '(x) = f '( g(x) ) g '(x)

In words: The derivative of h(x) is equal to the derivative of f with respect to g(x) TIMES the derivative of g(x) with respect to x.


Now, in this case, you want the derivative of h(x) = f (f(x) ).

We follow the same rule as above, exactly:

h '(x) = f' ( f(x) ) * f '(x)

Can you take the solution of this problem from here, or do you need and want further explanation? As one example, the value of f '(1) can be obtained from the given table and is 2.

Answer 18

Borrowed from Zardon:

h'(x)=f'(f(x))f'(x) then evaluate at x=1

In other words:

1) Find the value of f '(1) from the table. It is 2.
2) Find the value of f (1) from the table. It is 3.
3) This 3 is the input to f '(x). Find the value of f '(3) from the table. It is 7.

Now put this whole works together. What is the value of h(1)?