##
Maximum slope of the curve y = –x
^{
3
}
+ 3x
^{
2
}
+ 9x – 27 is:

## (A) 0 (B) 12

## (C) 16 (D) 32

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

NCERT Exemplar - MCQs

Question 1
Important

Question 2 Important

Question 3 Important

Question 4 Important

Question 5 Important

Question 6

Question 7 Important

Question 8 Important

Question 9 Important

Question 10

Question 11 Important

Question 12 Important

Question 13

Question 14

Question 15 Important You are here

Question 16 Important

Question 17 Important

Question 1 Important Deleted for CBSE Board 2024 Exams

Question 2 Deleted for CBSE Board 2024 Exams

Question 3 Important Deleted for CBSE Board 2024 Exams

Question 4 Deleted for CBSE Board 2024 Exams

Question 5 Deleted for CBSE Board 2024 Exams

Question 6 Deleted for CBSE Board 2024 Exams

Question 7 Important Deleted for CBSE Board 2024 Exams

Question 8 Deleted for CBSE Board 2024 Exams

Question 9 Important Deleted for CBSE Board 2024 Exams

Question 10 Important Deleted for CBSE Board 2024 Exams

Question 11 Deleted for CBSE Board 2024 Exams

Question 12 Deleted for CBSE Board 2024 Exams

Question 13 Deleted for CBSE Board 2024 Exams

Chapter 6 Class 12 Application of Derivatives

Serial order wise

Last updated at May 29, 2023 by Teachoo

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Question 15 Maximum slope of the curve y = βx3 + 3x2 + 9π₯ β 27 is: 0 (B) 12 (C) 16 (D) 32 Given y = β π₯^3 + 3π₯^2 + 9π₯β 27 Now, Slope of the curve =π π/π π = β3π₯^2 + 6π₯+ 9 We need to find maximum slope Letβs assume π(π) = Slope Thus, we need to maximize π(π₯) Maximizing π(π) π(π₯) = β3π₯^2 + 6π₯+ 9 Finding πβ(π) π^β² (π)=β6π₯+6 =βπ(πβπ) Putting π^β² (π)=π β6 (π₯β1) = 0 π₯β1 = 0 π = 1 Finding sign of gβ(π) at x = 1 gβ(π₯) = β6 < 0 Since gββ(x) < 0 at x = 1 β΄ g is maximum at x = 1 Finding Maximum Value of g(x) g(1) = "β3 " γ(1)γ^2 "+ 6 (1) + 9" = β3 + 6 + 9 = β3 + 15 = 12 Hence, Maximum slope = Maximum value of g(x) = 12 So, the correct answer is (B)