JEE Mains · Maths · STD 12 - 6. Application of derivatives
Let \(f : R \rightarrow R\) be defined as, \(f(x)=\left\{\begin{array}{ll}-55 x, & \text { if } x<-5 \\ 2 x^{3}-3 x^{2}-120 x, & \text { if }-5 \leq x \leq 4 \\ 2 x^{3}-3 x^{2}-36 x-336, & \text { if } x>4\end{array}\right.\) Let \(A=\{ x \in R : f\) is increasing \(\} .\) Then \(A\) is equal to :
- A \((-\infty,-5) \cup(4, \infty)\)
- B \((-5, \infty)\)
- C \((-\infty,-5) \cup(-4, \infty)\)
- D \((-5,-4)\cup(4, \infty)\)
Answer & Solution
Correct Answer
(D) \((-5,-4)\cup(4, \infty)\)
Step-by-step Solution
Detailed explanation
\(f(x)=\left\{\begin{array}{ll}-55 x, & \text { if } x<-5 \\ 6(x-5)(x+4), & \text { if }-5 \leq x \leq 4 \\ 6(x-5)(x+4), & \text { if } x>4\end{array}\right.\) \(f ( x )\) is increasing in \(x \in(-5,-4) \cup(4, \infty)\)
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