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Let f(x)=4x2−4ax+a2−2a+2 such that minimum value of f(x) for x∈[0,2] is equal to 3.Number of values of a for which global minimum value, that is equal to 3 for x∈[0,2], occurs at the end point of interval [0, 2] isNumber of values of a for which global minimum value, that is equal to 3 for x∈[0,2], occurs for the value of x lying in (0, 2) isValues of a for which f(x) is monotonic for x∈[0,2] are given by

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a≤0 or a≥4

0≤a≤4

a > 0

none of these

answer is , , .

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f(x)=4x2−4ax+a2−2a+2 represents a parabola whose vertex is at a2,2−2a.Case I: 0

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