Consider the following statements :
S 1 : The function y = 
is neither increasing nor decreasing.
S 2 : If f(x) is strictly increasing real function defined on R and c is a real constant, then number of Solutions of f(x) = c is always equal to one.
S 3 : Let f(x) = x ; x ∈ (0, 1). f(x) does not has any point of local maxima/minima
S 4 : f(x) = {x} has maximum at x = 6 (here {.} denotes fractional part function).
State, in order, whether S 1 , S 2 , S 3 , S 4 are true or false
S 1 , S 2 , S 3 , S 4 ds ; (T) ; (F)
Text Solution
Verified by ExpertsC
S 1 y = 
is even funciton.
Even function is nonmonotonic.
S 2 If range of f(x) is not R and c does not belong to range of f(x) then it is not necessary to have one
S 3 f ′ (x) = 1 > 0
f(x) is increasing
f(0), f(1) is not defined. Hence no local maxima/minima.
f ′ (x) = 1 > 0
f(x) o)SA
S 4 f(6) = 0 ; f(6 – h) > f(6)
& f(6 + h) > f(6)
Minima at x = 6 x = 6 ij
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