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Question

f(x) = x2 4|x| and g(x) = {min{f(t) : 6 t x}, x ϵ [6, 0]max{f(t) : 0 t x}, x ϵ [0, 6], than g(x)

A
Exactly one point of local minima
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B
Exactly one point of local maxima
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C
No point of local maxima but exactly one point of local minima
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D
Neither a point of local maxima nor minima
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Solution

The correct option is D Neither a point of local maxima nor minima

Bold line represents the graph of y = g(x) clearly g(x) has neither a point of local maxima nor a point of local minima.


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