Function game

Calculus Level 5

Let f f be a twice differentiable function on the open interval ( − 1 , 1 ) (-1,1) such that f ( 0 ) = 1 f(0)=1 . If f ( x ) ≥ 0 f(x)\ge 0 , f ′ ( x ) ≤ 0 f'(x)\le 0 and f ′ ′ ( x ) ≤ f ( x ) f''(x)\le f(x) for all x ≥ 0 x \ge 0 , find the minimum possible value of f ′ ( 0 ) f'(0) .


The answer is -1.4142.

Rajdeep Brahma by rajdeep brahma , 21, India

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1 solution

Rajdeep Brahma
Jun 10, 2018

This is an ISI ENTRANCE 2011 subjective ripper.Sorry for the inverted image tho :(

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where may i find previous ISI exam?

D S - 2 years, 12 months ago

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U mean the papers?U can easily get them in net...but for solutions see aops if u wish...it has got solutions from 2011....in net also there is a guy called amit ghosh who provides solutions till 2009....so u will have to get like this since isi don't publish any official solution.U may also try out past year cmi papers the advantage of which is that there is an official solution to each paper.

rajdeep brahma - 2 years, 12 months ago

Yes same solution

Suhas Sheikh - 2 years, 11 months ago

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