MHT CET · Maths · Application of Derivatives
For every value of \(x \in[1,3]\), the function \(f(x)=\frac{1}{8^x}\) is
- A increasing for \(x>2\) and decreasing for \(x \leq 2\).
- B neither increasing nor decreasing.
- C decreasing.
- D increasing.
Answer & Solution
Correct Answer
(C) decreasing.
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & f(x)=\frac{1}{8^x}=8^{-x} \\ & \Rightarrow f^{\prime}(x)=8^{-x} \log 8 \times(-1) \\ & \Rightarrow f^{\prime}(x)=\frac{-\log 8}{8^x}<0 \forall x \in[1,3] \\ & \Rightarrow f(x) \text { is decreasing } \forall x \in[1,3]\end{aligned}\)
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