Class 12 Applications Of Derivatives · Assertion Reason1 Marksassertion_reason

Class 12 Maths · Applications Of Derivatives · Assertion Reason #25

Assertion: The function f(x)=x⁴ is decreasing on (0,∞). Reason: If a differentiable function has f′(x)<0 throughout an interval, it is strictly decreasing there.

(A) Both A and R are true, and R correctly explains A.
(B) Both A and R are true, but R does not correctly explain A.
(C) A is true, but R is false.
(D) A is false, but R is true.

✅ Step-by-Step Solution

Final Answer: Option (D): A is false, but R is true.

f′=4x³>0 for x>0, so A is false; the sufficient condition R is true.

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Class 12 Maths · Applications Of Derivatives · Assertion Reason #25

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