Let a function f : R R be defined as f(x) = _ 0 ^ x (5 − |t − 3|)dt for x > 4 and f(x) = x^ 2 + bx for x 4. Where b R, If f is continuous at x = 4 then which of the following statements is NOT true ?

JEE Main 2022 Mathematics question

Let a function f : be defined as − |t − 3|)dt for x > 4 and + bx for . Where b R, If f is continuous at x = 4 then which of the following statements is NOT true ?

(1)f is not differentiable at x = 4
(2)
(3)f is increasing in (, 1/8) (8, )Correct
(4)f has a local minima at x = 1/8

Answer: (3)

Solution

Continuity at x = 4: − |t − 3|)dt = , so b = −1/4. Then for x > 4 and 2x − 1/4 for , so and ,

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Question ID VK-034435