Table Where f is differentiable

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HCL

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May 18, 2013
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21
x f f '
1 2 3
2 1 4

Given the table above, where f is differentiable, find the derivative of f(f(x)) at x = 2.
A. 3
B. 4
C. 8
D. 12

So I did this two dif ways, one got me 4, which is wrong, and the other, which I thought was write, doesn't make sense.

I used the x,f, as coordinates for slope form (1-2)/(2-1)=-1 then i put that in y=-x+b, put in the coordinates and got b=3, so

y=-x+3, which satifies the coorindates BUT, when I look for the derivative, y'=-x^0+3 (2,1), f' doesn't equal 4...

i also tried placing f(f(x))= -(x+3)+3=-x and then the derivative would be f'(f(x))=1... ugh i have no clue, i googled, etc, can't figure it out
 
HCL said:
x f f '
1 2 3
2 1 4

Given the table above, where f is differentiable, find the derivative of f(f(x)) at x = 2.
A. 3
B. 4
C. 8
D. 12

So I did this two dif ways, one got me 4, which is wrong, and the other, which I thought was write, doesn't make sense.

I used the x,f, as coordinates for slope form (1-2)/(2-1)=-1 then i put that in y=-x+b, put in the coordinates and got b=3, so

y=-x+3, which satifies the coorindates BUT, when I look for the derivative, y'=-x^0+3 (2,1), f' doesn't equal 4...

i also tried placing f(f(x))= -(x+3)+3=-x and then the derivative would be f'(f(x))=1... ugh i have no clue, i googled, etc, can't figure it out
Click to expand...

Use the chain rule.

\(\displaystyle \dfrac{d}{dx} f(f(x)) = f'(f(x))\cdot f'(x)\)
 
HCL said:
x f f '
1 2 3
2 1 4

Given the table above, where f is differentiable, find the derivative of f(f(x)) at x = 2.
Click to expand...
Over-thinking it, perhaps.

At x=2, f(x) = 1, and f'(1) = 3.
 
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