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Let be a differentiable function such that f'(x) > f(x) for all and f(0) = 1. Then f( 1) lies in the interval

  • a)
    (0, e−1)

  • b)
    (0, e−1, √e)

  • c)
    (e, ∞)

  • d)
    (√e, e)

Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Let be a differentiable function such that f(x) > f(x) for all an...
Let be defined as
f(x) = eax, a > 1 x ← R
f′(x) = aeax.
f(o) = aeao = 1 & f′(x) = aeax > eax = f(x) ∀ x ∈ R.
hence f(1) = ea
.
e < ea < ∞
⇒ f(1). lies in the interval (e, ∞)
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Most Upvoted Answer
Let be a differentiable function such that f(x) > f(x) for all an...
Let be defined as
f(x) = eax, a > 1 x ← R
f′(x) = aeax.
f(o) = aeao = 1 & f′(x) = aeax > eax = f(x) ∀ x ∈ R.
hence f(1) = ea
.
e < ea < ∞
⇒ f(1). lies in the interval (e, ∞)
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Question Description
Let be a differentiable function such that f(x) > f(x) for all and f(0) = 1. Then f( 1) lies in the intervala)(0, e−1)b)(0, e−1,√e)c)(e, ∞)d)(√e, e)Correct answer is option 'C'. Can you explain this answer? for IIT JAM 2025 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about Let be a differentiable function such that f(x) > f(x) for all and f(0) = 1. Then f( 1) lies in the intervala)(0, e−1)b)(0, e−1,√e)c)(e, ∞)d)(√e, e)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for IIT JAM 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let be a differentiable function such that f(x) > f(x) for all and f(0) = 1. Then f( 1) lies in the intervala)(0, e−1)b)(0, e−1,√e)c)(e, ∞)d)(√e, e)Correct answer is option 'C'. Can you explain this answer?.
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