The function f(x)=2 x^3-15 x^2+36 x+6 is increasing in the ...

CBSE Class 12 Math 2022 Term I Solved Paper

SECTION - B In this Section attempt any 16 questions out of the Questions 21-40. Each question is of one mark .

Question : 21 of 50

Marks: +1, -0

The function

f(x)=2 x^3-15 x^2+36 x+6

is increasing in the interval

Solution: 👈: Video Solution

Explanation: Given,

f(x)=2 x^3-15 x^2+36 x+6

∴ \;\; f^{'}(x)=6 x^2-30 x+36

f^{'}(x) ≥ 0

, then

f(x)

is increasing.
So,

\;\; 6 x^2-30 x+36 ≥ 0

\;\text " or, "\;\;x^2-5 x+6 ≥ 0

\;\text " or, "\;\;(x-3)(x-2) ≥ 0

∴ \;x\;∈(-∞, 2] ∪[3, ∞)

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