Let f: R→R be a function defined by f(x)=Max{x,x3} then
A
f (x) is discontinuous at 3 points
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B
f (x) is not differentiable at 3 points
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C
f(x) is continuous at all points
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D
f (x) is not differentiable at x = 0
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Solution
The correct options are B f (x) is not differentiable at 3 points C f(x) is continuous at all points D f (x) is not differentiable at x = 0 Clearly not differentiable at x=0,±1 2nd method Solving x3=x, we have x=0,±1 ∴Max{x,x2}=x When x < -1 =x3 when −1≤x≤0 =x when 0 < x≤1 =x^3 when x > 1