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99 Percentile Qs Bank for JEE MainMathematicsApplication of Derivatives

For the following questions, choose the correct answers from the codes (a), (b), (c) and (d) defined as follows: Statement I: ϕ x = ∫ 0 x 3 sin t + 4 cos t   d t , π 6 , π 3 .   ϕ x   attains its maximum value at x = π 3 . Statement II: ϕ x = ∫ 0 x 3 s i n t + 4 c o s t   d t ,   ϕ x is increasing function in π 6 , π 3 .

Options

  1. AStatement I is true. Statement II is also true. Statement II is the correct explanation of Statement I.
  2. BStatement I is true. Statement II is also true. Statement II is not the correct explanation of Statement I.
  3. CStatement I is true. Statement II is false.
  4. DStatement I is false. Statement II is true.

Correct answer

A. Statement I is true. Statement II is also true. Statement II is the correct explanation of Statement I.

Step-by-step solution

ϕ ( x ) = ∫ 0 x ( 3 sin t + 4 cos t ) d t Differentiate w.r.t. x , ϕ ' ( x ) = 3 sin x + 4 cos x ϕ ' ( x ) > 0         ∀   x ∈   π 6 , π 3 ⇒ ϕ ( x ) is an increasing function in interval π 6 , π 3 . ⇒ ϕ ( x ) attains maximum value at x = π 3 .

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