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Application of Derivatives question

2021 · 24 Feb · Shift 2 · Q29
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  5. /2021 · 24 Feb · Shift 2 · Q29

Application of Derivatives question

2021 · 24 Feb · Shift 2 · Q29

JEE MainMathematicsApplication of DerivativesMCQ+4 / −1
Let f:R→Rf:R \to Rf:R→R be defined as f(x)={−55x,if x<−52x3−3x2−120x,if −5≤x≤42x3−3x2−36x−336,if x>4,f(x) = \left\{ {\begin{matrix} { - 55x,} & {if\,x \lt - 5} \\ {2{x^3} - 3{x^2} - 120x,} & {if\, - 5 \le x \le 4} \\ {2{x^3} - 3{x^2} - 36x - 336,} & {if\,x \gt 4,} \\ \end{matrix} } \right.f(x)=⎩⎨⎧​−55x,2x3−3x2−120x,2x3−3x2−36x−336,​ifx<−5if−5≤x≤4ifx>4,​ Let A = {x ∈\in∈ R : f is increasing}. Then A is equal to :
  1. A
    (−5,∞)( - 5,\infty )(−5,∞)
  2. B
    (−∞,−5)∪(4,∞)( - \infty , - 5) \cup (4,\infty )(−∞,−5)∪(4,∞)
  3. C
    (−5,−4)∪(4,∞)( - 5, - 4) \cup (4,\infty )(−5,−4)∪(4,∞)
  4. D
    (−∞,−5)∪(−4,∞)( - \infty , - 5) \cup ( - 4,\infty )(−∞,−5)∪(−4,∞)
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