AP EAMCET · Maths · Application of Derivatives
The function \(f(x)=(1 / 2)^x\) on \(R\) is
- A Strictly decreasing
- B Strictly increasing
- C Decreasing
- D Neither increasing nor decreasing
Answer & Solution
Correct Answer
(A) Strictly decreasing
Step-by-step Solution
Detailed explanation
Let \(y=\left(\frac{1}{2}\right)^x\) on \(R\) \(\frac{d y}{d x}=\left(\frac{1}{2}\right)^x \log \frac{1}{2}=-\left(\frac{1}{2}\right)^x \log 2\) \(\left(\frac{d y}{d x} < 0\right)\) so strictly decreasing
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