unsure of how to begin this problem...

[Guest]

Here is the stuff...

This problem tests calculating new functions from old ones:

From the table below calculate the quantities asked for:

x 8 10 6
-----------------------
f(x) 10 0.5 3.5
g(x) 6 1.5 1
f'(x) -7 -1 3
g'(x) -0.5 0.5 1.5

If h(x) = f(x)/g(x). calculate h'(8)
If h(x) = g(f(x)), calculate h'(8)
f(f(8))

I did the first one and I did it correctly, but the others I'm still confused about...

Any help is appreciated...

 

[stapel]

For the second and third parts, use the Chain Rule, and plug in the appropriate values from the table.

Eliz.

 

[Guest]

I'm not sure if I understand how to apply the chain rule to those functions...

 

[pka]

plug in the appropriate values from the table.

\(\displaystyle \L
\begin{array}{l}
h(x) = \frac{{f(x)}}{{g(x)}}\quad \Rightarrow \quad h'(x) = \frac{{f'(x)g(x) - f(x)g'(x)}}{{\left( {g(x)} \right)^2 }} \\
h(x) = g(f(x))\quad \Rightarrow \quad h'(x) = g'(f(x))f'(x) \\
h(x) = f(f(x))\quad \Rightarrow \quad h'(x) = f'(f(x))f'(x) \\
\end{array}\)

 

[Guest]

what do I plug in for g'(f(x)) and f'(f(x)) - that is where my problem is...

 

[pka]

\(\displaystyle \L
f(8) = 10\quad ,\quad g'(10) = ?\quad \& \quad f'(10) = ?\)

 

[Guest]

thank you!