Question

4. Suppose that $h$ and $g$ are differentiable functions with the values shown in the following table: egin{tabular}{|c|c|c|c|c|} hline $x$ & 1 & 2 & 3 & 4 \ hline $h(x)$ & 2 & 3 & 4 & 1 \ hline $h'(x)$ & 3 & 5 & 2 & -2 \ hline $g(x)$ & 1 & 4 & 1 & 2 \ hline $g'(x)$ & 4 & -2 & -1 & 3 \ hline end{tabular} Show all work. You do not need to simplify your numerical answer. (a) [7pts] Find $f'(2)$ if $f(x) = 3h(x)g(x)$. (b) [7pts] Find $f'(3)$ if $f(x) = frac{g(x)}{h(x) + 2}$. (c) [7pts] Find $f'(1)$ if $f(x) = g(x + h(x))$.

          4. Suppose that $h$ and $g$ are differentiable functions with the values shown in the following table:

egin{tabular}{|c|c|c|c|c|}
hline
$x$ & 1 & 2 & 3 & 4 \
hline
$h(x)$ & 2 & 3 & 4 & 1 \
hline
$h'(x)$ & 3 & 5 & 2 & -2 \
hline
$g(x)$ & 1 & 4 & 1 & 2 \
hline
$g'(x)$ & 4 & -2 & -1 & 3 \
hline
end{tabular}

Show all work. You do not need to simplify your numerical answer.
(a) [7pts] Find $f'(2)$ if $f(x) = 3h(x)g(x)$.
(b) [7pts] Find $f'(3)$ if $f(x) = frac{g(x)}{h(x) + 2}$.
(c) [7pts] Find $f'(1)$ if $f(x) = g(x + h(x))$.

$4. Suppose that h and g are differentiable functions with the values shown in the following table: egintabular|c|c|c|c|c| hline x 1 2 3 4 hline h(x) 2 3 4 1 hline h'(x) 3 5 2 -2 hline g(x) 1 4 1 2 hline g'(x) 4 -2 -1 3 hline endtabular Show all work. You do not need to simplify your numerical answer. (a) [7pts] Find f'(2) if f(x) = 3h(x)g(x). (b) [7pts] Find f'(3) if f(x) = fracg(x)h(x) + 2. (c) [7pts] Find f'(1) if f(x) = g(x + h(x)).$

Added by Ivan H.

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