APFIVE Quotient Rule Using a Table
The table below provides values for the twice-differentiable functions $$f$$ and $$g$$, and their derivatives, at $$x = 3$$.
| $$x$$ | $$f(x)$$ | $$f'(x)$$ | $$f''(x)$$ | $$g(x)$$ | $$g'(x)$$ | $$g''(x)$$ |
|---|---|---|---|---|---|---|
| 3 | 2 | -1 | 4 | 5 | -3 | -2 |
If $$h(x) = \displaystyle\frac{g'(x)}{f(x)}$$, what is the value of $$h'(3)$$?
A
$$\displaystyle\frac{5}{4}$$
B
$$\displaystyle\frac{1}{4}$$
C
$$-\displaystyle\frac{7}{4}$$
D
$$-\displaystyle\frac{1}{2}$$
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