Please Help with CALC test question...? Tricky!!!?

I

Isabella

New member
Let f,g and their derivatives be defined by the table below. Whats the derivative of f(g(x)) at x=2?
Table:
X 1 2 3 4
f(x) 3 0 1 2
g(x) 2 3 4 1
f'(x) 1 2 3 1
g'(X) 2 2 1 1
A.6
B2
C.8
D.4
E.0
please help thanks!
 
Hi Isabella,

We need to find the derivative of f(g(x)) at x=2, in other words, the derivative of f(g(2)). From the chain rule, we know that the derivative of f(g(2)) is equal to f'(g(2))*g'(2). From the table, we see that g(2) is 3, so f'(g(2))*g'(2) can be rewritten as f'(3)*g'(2). We also know from the table that f(3)=1 and g'(2)=2, so f'(3)*g'(2)=1*2=2. Therefore, the derivative f(g(x)) at x=2 is 2, so choice B is correct.

I hope that helps :)
 
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