What is f'(-1) equal to?
For the following two (02) items: Consider the function f(x)=\begin{cases}4(5^{x}),&x \lt 0\\ 8k+x,&x \geq 0\end{cases}
- A. \frac{2}{5}\ln 5
- B. \frac{3}{5}\ln 5
- C. \frac{4}{5}\ln 5 ✓
- D. 20\ln 5
Correct Answer: C. \frac{4}{5}\ln 5
Explanation
For x \lt 0, the function is defined as f(x) = 4(5^x). Differentiating with respect to x yields f'(x) = 4(5^x \ln 5). Substituting x = -1, we get f'(-1) = 4(5^{-1} \ln 5) = \frac{4}{5} \ln 5.
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