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Let f : ℝ → ℝ be continuous on ℝ and differentiable on (−∞, 0) ∪ (0, ∞). Which of the following statements is (are) always TRUE?a)If
is differentiable at 0 and f′(0) = 0, then
has a local maximum or a local minimum at 0b)If fhas a local minimum at 0, then fis differentiable at 0 and f′(0) = 0c)If f′(x) < 0 for all x< 0 and f′ (x) > 0 for all x> 0, then fhas a global maximum at 0d)If f′ (x) > 0 for all x< 0 and f′(x) < 0 for all x> 0, then fhas a global maximum at 0Correct answer is option 'D'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about Let f : ℝ → ℝ be continuous on ℝ and differentiable on (−∞, 0) ∪ (0, ∞). Which of the following statements is (are) always TRUE?a)If
is differentiable at 0 and f′(0) = 0, then
has a local maximum or a local minimum at 0b)If fhas a local minimum at 0, then fis differentiable at 0 and f′(0) = 0c)If f′(x) < 0 for all x< 0 and f′ (x) > 0 for all x> 0, then fhas a global maximum at 0d)If f′ (x) > 0 for all x< 0 and f′(x) < 0 for all x> 0, then fhas a global maximum at 0Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f : ℝ → ℝ be continuous on ℝ and differentiable on (−∞, 0) ∪ (0, ∞). Which of the following statements is (are) always TRUE?a)If
is differentiable at 0 and f′(0) = 0, then
has a local maximum or a local minimum at 0b)If fhas a local minimum at 0, then fis differentiable at 0 and f′(0) = 0c)If f′(x) < 0 for all x< 0 and f′ (x) > 0 for all x> 0, then fhas a global maximum at 0d)If f′ (x) > 0 for all x< 0 and f′(x) < 0 for all x> 0, then fhas a global maximum at 0Correct answer is option 'D'. Can you explain this answer?.

Solutions for Let f : ℝ → ℝ be continuous on ℝ and differentiable on (−∞, 0) ∪ (0, ∞). Which of the following statements is (are) always TRUE?a)If
is differentiable at 0 and f′(0) = 0, then
has a local maximum or a local minimum at 0b)If fhas a local minimum at 0, then fis differentiable at 0 and f′(0) = 0c)If f′(x) < 0 for all x< 0 and f′ (x) > 0 for all x> 0, then fhas a global maximum at 0d)If f′ (x) > 0 for all x< 0 and f′(x) < 0 for all x> 0, then fhas a global maximum at 0Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for IIT JAM. Download more important topics, notes, lectures and mock test series for IIT JAM Exam by signing up for free.

Here you can find the meaning of Let f : ℝ → ℝ be continuous on ℝ and differentiable on (−∞, 0) ∪ (0, ∞). Which of the following statements is (are) always TRUE?a)If
is differentiable at 0 and f′(0) = 0, then
has a local maximum or a local minimum at 0b)If fhas a local minimum at 0, then fis differentiable at 0 and f′(0) = 0c)If f′(x) < 0 for all x< 0 and f′ (x) > 0 for all x> 0, then fhas a global maximum at 0d)If f′ (x) > 0 for all x< 0 and f′(x) < 0 for all x> 0, then fhas a global maximum at 0Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Let f : ℝ → ℝ be continuous on ℝ and differentiable on (−∞, 0) ∪ (0, ∞). Which of the following statements is (are) always TRUE?a)If
is differentiable at 0 and f′(0) = 0, then
has a local maximum or a local minimum at 0b)If fhas a local minimum at 0, then fis differentiable at 0 and f′(0) = 0c)If f′(x) < 0 for all x< 0 and f′ (x) > 0 for all x> 0, then fhas a global maximum at 0d)If f′ (x) > 0 for all x< 0 and f′(x) < 0 for all x> 0, then fhas a global maximum at 0Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Let f : ℝ → ℝ be continuous on ℝ and differentiable on (−∞, 0) ∪ (0, ∞). Which of the following statements is (are) always TRUE?a)If
is differentiable at 0 and f′(0) = 0, then
has a local maximum or a local minimum at 0b)If fhas a local minimum at 0, then fis differentiable at 0 and f′(0) = 0c)If f′(x) < 0 for all x< 0 and f′ (x) > 0 for all x> 0, then fhas a global maximum at 0d)If f′ (x) > 0 for all x< 0 and f′(x) < 0 for all x> 0, then fhas a global maximum at 0Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Let f : ℝ → ℝ be continuous on ℝ and differentiable on (−∞, 0) ∪ (0, ∞). Which of the following statements is (are) always TRUE?a)If
is differentiable at 0 and f′(0) = 0, then
has a local maximum or a local minimum at 0b)If fhas a local minimum at 0, then fis differentiable at 0 and f′(0) = 0c)If f′(x) < 0 for all x< 0 and f′ (x) > 0 for all x> 0, then fhas a global maximum at 0d)If f′ (x) > 0 for all x< 0 and f′(x) < 0 for all x> 0, then fhas a global maximum at 0Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Let f : ℝ → ℝ be continuous on ℝ and differentiable on (−∞, 0) ∪ (0, ∞). Which of the following statements is (are) always TRUE?a)If
is differentiable at 0 and f′(0) = 0, then
has a local maximum or a local minimum at 0b)If fhas a local minimum at 0, then fis differentiable at 0 and f′(0) = 0c)If f′(x) < 0 for all x< 0 and f′ (x) > 0 for all x> 0, then fhas a global maximum at 0d)If f′ (x) > 0 for all x< 0 and f′(x) < 0 for all x> 0, then fhas a global maximum at 0Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice IIT JAM tests.