Definite IntegrationHard
Question
Let f(x) = 
∀ x ∈ (3, 4) , then the difference between the greatest and the least values of the function is
∀ x ∈ (3, 4) , then the difference between the greatest and the least values of the function isOptions
A.49/6
B.59/6
C.69/8
D.59/3
Solution
f′(x) = x2 - x + 1 > 0 ∀ x ∈ R
∵ f(x) is increasing in x ∈ (3, 4) so minimum at x = 3 and maximum at x = 4
∴ min f(x) =
=
max f(x) =
=
∴ max f(x) - min f(x) =
∵ f(x) is increasing in x ∈ (3, 4) so minimum at x = 3 and maximum at x = 4
∴ min f(x) =
=
max f(x) =
=
∴ max f(x) - min f(x) =
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