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Class 12 Applications Of Derivatives · Mcq Single Correct1 Marksmonotonicity

Class 12 Maths · Applications Of Derivatives · Mcq Single Correct #17

Which statement about f(x)=2x³−3x²−36x+7 is correct?

Derivative sign chart (mcq 17)

(A) Strictly increasing on (−∞,−2) and strictly decreasing on (−2,∞)
(B) Strictly decreasing on (−2,3)
(C) Strictly decreasing on (−∞,3) and strictly increasing on (3,∞)
(D) Strictly decreasing on each of (−∞,−2) and (3,∞)

✅ Step-by-Step Solution

Final Answer: Option (B): Strictly decreasing on (−2,3)

f′=6(x+2)(x−3) is negative between −2 and 3 and positive outside.

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