Last Updated On [03-11-2023]
Let 
be a non-constant thrice differentiable function defined on 
such that 
and 
. If 
is the minimum number or roots of 
in the interval [0, 6], then the value of 
is
Let be a non-constant thrice differentiable function defined on such that and . If is the minimum number or roots of in the interval [0, 6], then the value of is
Question ID - 153400 :-
Let be a non-constant thrice differentiable function defined on such that and . If is the minimum number or roots of in the interval [0, 6], then the value of is
|
Let |
|
(6)
On differentiating (1) w.r.t.
Putting
Similarly
Now, consider a function As So, by Rolle’s theorem, the equation Now Clearly Hence again by Rolle’s theorem, |
(1)
, we get
(2)
in (2), we get
has minimum 7 roots in [0, 6]
satisfy Rolle’s theorem in intervals 
and 
respectively
has minimum 6 roots
, where 
has minimum 13 roots in [0, 6]
has minimum 12 zeroes in [0, 6]Next Question :
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A right triangle is drawn in a semicircle of radius |
with one of its legs along the diameter. If the maximum area of the triangle is 
, then the value of 
isView Topper Answer
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