Question Description
Let f be a real-valued function of a real variable defined as f ( x) = x 2 for x ≥ 0 , and 2f ( x) =- x2 for x < 0 . Which one of the following statements is true?a)f (x) is discontinuous at x = 0 .b)f (x) is continuous but not differentiable at x = 0 .c)f (x) is differentiable but its first derivative is not continuous at x = 0 .d)f (x) is differentiable but its first derivative is not differentiable at x = 0Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Let f be a real-valued function of a real variable defined as f ( x) = x 2 for x ≥ 0 , and 2f ( x) =- x2 for x < 0 . Which one of the following statements is true?a)f (x) is discontinuous at x = 0 .b)f (x) is continuous but not differentiable at x = 0 .c)f (x) is differentiable but its first derivative is not continuous at x = 0 .d)f (x) is differentiable but its first derivative is not differentiable at x = 0Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f be a real-valued function of a real variable defined as f ( x) = x 2 for x ≥ 0 , and 2f ( x) =- x2 for x < 0 . Which one of the following statements is true?a)f (x) is discontinuous at x = 0 .b)f (x) is continuous but not differentiable at x = 0 .c)f (x) is differentiable but its first derivative is not continuous at x = 0 .d)f (x) is differentiable but its first derivative is not differentiable at x = 0Correct answer is option 'D'. Can you explain this answer?.

Solutions for Let f be a real-valued function of a real variable defined as f ( x) = x 2 for x ≥ 0 , and 2f ( x) =- x2 for x < 0 . Which one of the following statements is true?a)f (x) is discontinuous at x = 0 .b)f (x) is continuous but not differentiable at x = 0 .c)f (x) is differentiable but its first derivative is not continuous at x = 0 .d)f (x) is differentiable but its first derivative is not differentiable at x = 0Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE. Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.

Here you can find the meaning of Let f be a real-valued function of a real variable defined as f ( x) = x 2 for x ≥ 0 , and 2f ( x) =- x2 for x < 0 . Which one of the following statements is true?a)f (x) is discontinuous at x = 0 .b)f (x) is continuous but not differentiable at x = 0 .c)f (x) is differentiable but its first derivative is not continuous at x = 0 .d)f (x) is differentiable but its first derivative is not differentiable at x = 0Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Let f be a real-valued function of a real variable defined as f ( x) = x 2 for x ≥ 0 , and 2f ( x) =- x2 for x < 0 . Which one of the following statements is true?a)f (x) is discontinuous at x = 0 .b)f (x) is continuous but not differentiable at x = 0 .c)f (x) is differentiable but its first derivative is not continuous at x = 0 .d)f (x) is differentiable but its first derivative is not differentiable at x = 0Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Let f be a real-valued function of a real variable defined as f ( x) = x 2 for x ≥ 0 , and 2f ( x) =- x2 for x < 0 . Which one of the following statements is true?a)f (x) is discontinuous at x = 0 .b)f (x) is continuous but not differentiable at x = 0 .c)f (x) is differentiable but its first derivative is not continuous at x = 0 .d)f (x) is differentiable but its first derivative is not differentiable at x = 0Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Let f be a real-valued function of a real variable defined as f ( x) = x 2 for x ≥ 0 , and 2f ( x) =- x2 for x < 0 . Which one of the following statements is true?a)f (x) is discontinuous at x = 0 .b)f (x) is continuous but not differentiable at x = 0 .c)f (x) is differentiable but its first derivative is not continuous at x = 0 .d)f (x) is differentiable but its first derivative is not differentiable at x = 0Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Let f be a real-valued function of a real variable defined as f ( x) = x 2 for x ≥ 0 , and 2f ( x) =- x2 for x < 0 . Which one of the following statements is true?a)f (x) is discontinuous at x = 0 .b)f (x) is continuous but not differentiable at x = 0 .c)f (x) is differentiable but its first derivative is not continuous at x = 0 .d)f (x) is differentiable but its first derivative is not differentiable at x = 0Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice GATE tests.