Definite IntegrationHard

Question

Let f(x) = then f is

Options

A.continuous at x = 3/2
B.continuous at x = 3
C.differentiable at x = 3/2
D.differentiable at x = 0

Solution

f(x) = = 3x - x2
x > 3/2
f(x) =
= + x2 - 3x
f(x) =
Now this is continuous at x = and at x = 3 also differentiable at x = 0

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