NCERT Exemplar - MCQs
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Last updated at Dec. 16, 2024 by Teachoo
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This question is similar to Ex 6.2, 6 - Chapter 6 Class 12 - Application of Derivatives
Transcript
Question 4 The interval on which the function f(π₯) = 2π₯3 + 9π₯2 + 12π₯ - 1 is decreasing is: (A) [β1,β) (B) [β2, β1] (C) (ββ,β2] (D) [β1, 1] f(π₯) = 2π₯3 + 9π₯2 + 12π₯ - 1 Calculating fβ(π) fβ(π₯) = 6π₯2 +18π₯ + 12 - 0 fβ(π₯) = 6(π₯2+3π₯+2) fβ(π₯) = 6(π₯2+2π₯+π₯+2) fβ(π₯) = 6(π₯(π₯+2)+1(π₯+2)) fβ(π) = 6(π+π) (π+π) Putting fβ(π) = 0 6(π₯+1) (π₯+2) = 0 (π₯+1) (π₯+2) = 0 So, π = β1 , β2 Plotting points on number line Hence, f is decreasing for the interval (β2, β1). So, the correct answer is (B)
