AP EAMCET · Maths · Application of Derivatives
If a number is drawn at random from the set \(\{1,3,5,7\), \(\ldots, 59\}\), then the probability that it lies in the interval in which the function \(f(x)=x^3-16 x^2+20 x-5\) is strictly decreasing, is
- A \(\frac{1}{5}\)
- B \(\frac{1}{3}\)
- C \(\frac{1}{2}\)
- D \(\frac{1}{6}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{6}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } f(x)=x^3-16 x^2+20 x-5 \\ & f^{\prime}(x)=3 x^2-32 x+20=(3 x-2)(x-10) \\ & f^{\prime}(x) \lt 0 \\ & x \in\left(\frac{2}{3}, 0\right) \Rightarrow x \text { can take values } 1,3,5,7,9 \\ & n(\mathrm{~S})=30, n(\mathrm{E})=5 \\ & \text { Required…
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