Question 17 - NCERT Exemplar - MCQs - Chapter 6 Class 12 Application of Derivatives (Term 1)
Last updated at Oct. 13, 2021 by Teachoo

The interval on which the function
f
(x) = 2x
^{
3
}
+ 9x
^{
2
}
+ 12x - 1 is decreasing is:
(A) [-1,∞)
(B) [–2, –1]
(C) (-∞,-2]
(D) [–1, 1]

This question is similar to
Ex 6.2, 6 - Chapter 6 Class 12
- Application of Derivatives

Transcript

Question 17
The interval on which the function f(๐ฅ) = 2๐ฅ3 + 9๐ฅ2 + 12๐ฅ - 1
is decreasing is:
(A) [โ1,โ) (B) [โ2, โ1]
(C) (โโ,โ2] (D) [โ1, 1]
f(๐ฅ) = 2๐ฅ3 + 9๐ฅ2 + 12๐ฅ - 1
Calculating fโ(๐)
fโ(๐ฅ) = 6๐ฅ2 +18๐ฅ + 12 - 0
fโ(๐ฅ) = 6(๐ฅ2+3๐ฅ+2)
fโ(๐ฅ) = 6(๐ฅ2+2๐ฅ+๐ฅ+2)
fโ(๐ฅ) = 6(๐ฅ(๐ฅ+2)+1(๐ฅ+2))
fโ(๐) = 6(๐+๐) (๐+๐)
Putting fโ(๐) = 0
6(๐ฅ+1) (๐ฅ+2) = 0
(๐ฅ+1) (๐ฅ+2) = 0
So, ๐ฅ = โ1 , โ2
Plotting points on number line
Hence, f is decreasing for the interval (โ2, โ1).
So, the correct answer is (B)

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