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Class 12 Applications Of Derivatives · Assertion Reason1 Marksassertion_reason

Class 12 Maths · Applications Of Derivatives · Assertion Reason #24

Assertion: The function f(x)=tan x−x is strictly increasing on each interval (−π/2+kπ,π/2+kπ), k∈Z. Reason: A differentiable function with nonnegative derivative and only isolated zeros of its derivative on an interval is strictly increasing there.

✅ Step-by-Step Solution

Final Answer: Option (A): Both A and R are true, and R correctly explains A.
  1. f′=tan²x≥0 on each stated interval and vanishes only at x=kπ. The integral of f′ on every nontrivial subinterval is positive.

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