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