A calculus problem by akash mahor
Calculus
Level
3
If rolle's theorem is applicable for f(x)= (x>0) in interval [a,b] where a,b=integer then value of is
The answer is 20.
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1 solution
ln(x)/x= -infinity (when x tends to zero)
ln(1)/1 = 0
max of ln(x)/x is at x = e (by differentiating)
ln(x)/x = 0 (when x tends to infinity)
Therefore function increases from 0 to e and then decreases(but remains positive after x= e)
ln(x)/x is continuos and differentiable at all x in domain
Therefore only condition is f(a) = f(b)
Between 1 and e the only integer is x=2 f(2) = ln(2)/2 and f(4) = ln(2)/2