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Use the table below with selected values of the twice differentlable function k Reach each explanation and decide whether you would apply IVT EVT or MVT X K x I 5 2 2 3 4 4 4 applies 5 3 6 2 7 O 6 Since k is differentiable it is also continuous Since k 6 2 and k 7 0 and since I is between 2 and O It follows by that K c 1 for some c between 6 and 7 7 Since k is differentiable and therefore also continuous and since 3 k 2 6 it follows by that k c 6 for some 3 2 c in the interval 2 3 8 There must be a minimum value for k at some r in 1 7 because k is differentiable and therefore also continuous Hence the q There must be some value a in 2 6 for which k a 0 because k 2 k 6 and since k is differentiable the applies 10 Since k is differentiable the guarantees some a in 4 5 for which k a 4 and also some b in 5 6 for which k b 1 Then since k is differentiable and therefore also continuous it follows by the applied to k that k c 0 for therefore in 46
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