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Suppose f is a twice differentiable function such that f′(x)>0 and f′′(x)<0 everywhere, and consider the...

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Basic Math

Suppose f is a twice differentiable function such thatf′(x)>0 and f′′(x)<0 everywhere, and consider the followingdata table.

x     0      1       2

f(x)   3      A       B

For each part below, determine whether the given values of A andB are possible (i.e., consistent with the information about f′andf′′ given above) or impossible, and explain your answer.

a)A= 5, B= 6

(b)A= 5, B= 8

(c)A= 6, B= 6

(d)A= 6, B= 6.1

(e)A= 6, B= 9

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