Consider the function f(x) = \left[\right. x \left{\right. x \left.\right} + 1 , 0 \leq x < 1 \\ 2 - \left{\right. x \left.\right} , 1 \leq x \leq 2 where {} denotes fractional part of function. Then

Engineering

Mathematics

Maxima and Minima

Question

Consider the function f(x) = $[\begin{array}{l} x {x} + 1, 0 \leq x < 1 \\ 2 - {x}, 1 \leq x \leq 2 \end{array}$
where {} denotes fractional part of function. Then

f(x) has exactly two points of local maxima

f(x) has exactly one point of local minima.

f(x) is monotonic in [0, 1].

Rolle's Theorem is applicable to f(x) in [0, 2]

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$f (x) = [\begin{array}{l} x^{2} + 1, [0, 1) \\ 3 - x, [1, 2) \\ 2, x = 2 \end{array}$

x = 0 is the point of local minima and x = 1 and 2 are the point of local maxima.