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Question

# Find the percentage rate of change of f(x) at the indicated value of x. Round to the nearest tenth of a percent. f(x)=75+110x; x=16

Solution

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To find the percentage rate of change of a function $f(x)$ we use the formula: $\frac{f'(x)}{f(x)}$. Therefore we need to find the logarithmic derivative f(x):

$\frac{d}{dx}\ln f(x)=\frac{110}{75+110x}$

By substituting $x=16$ and multiplying by $100$% we get:

$\frac{d}{dx}\ln f(16) \cdot 16\%= 5,99 \%$

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