Applying the Quotient Rule with Tabular Data

Question

The table provides values for the twice-differentiable functions $$f$$ and $$g$$ and their derivatives at $$x = -2$$:

| $$x$$ | $$f(x)$$ | $$f'(x)$$ | $$f''(x)$$ | $$g(x)$$ | $$g'(x)$$ | $$g''(x)$$ |
|-----|--------|---------|----------|--------|---------|----------|
| -2  |   1    |    3    |   -1     |   2    |   -1    |    2     |

Let the function $$h$$ be defined by $$h(x) = \displaystyle\frac{f(x) \cdot g'(x)}{g(x) \cdot f'(x)}$$. What is the value of $$h'(-2)$$?

Accepted Answer

$$-\displaystyle\frac{11}{36}$$

Answer

$$\displaystyle\frac{1}{6}$$

Answer

$$-\displaystyle\frac{5}{36}$$

Answer

$$\displaystyle\frac{7}{36}$$

Applying the Quotient Rule with Tabular Data

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