WBJEE · Maths · Application of Derivatives
Let \(f(x)=(x-2)^{17}(x+5)^{24}\). Then
- A \(f\) does not have a critical point at \(x=2\)
- B \(f\) has a minimum at \(x=2\)
- C \(f\) has neither a maximum nor a minimum at \(x=2\)
- D f has a maximum at \(x=2\)
Answer & Solution
Correct Answer
(C) \(f\) has neither a maximum nor a minimum at \(x=2\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & f(x)=(x-2)^{17}(x+5)^{24} \\ \Rightarrow & f^{\prime}(x)=17(x-2)^{16}(x+5)^{24}+24(x-2)^{17}(x+5)^{23}=(x-2)^{16}(x+5)^{23}(17 x+85+24 x-48)=(x-2)^{16}(x+5)^{23}(41 x+37) \end{aligned}\)
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