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Let be a function. Then which of the following statements is/are TRUE ?
  • a)
    If f is differentiable at (0, 0), then all directional derivatives of f exist at (0, 0).
  • b)
    If all directional derivatives of f exist at (0, 0), then f is differentiable at (0, 0).
  • c)
    If all directional derivatives of f exist at (0, 0), then f is continuous at (0, 0).
  • d)
    If the partial derivatives exist  and are continuous in a disc centered at (0,
    0) then f is differentiable at (0, 0).
Correct answer is option 'A,D'. Can you explain this answer?
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Let be a function. Then which of the following statements is/are TRUE...
By defn of partial derivatives
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Let be a function. Then which of the following statements is/are TRUE ?a)If f is differentiable at (0, 0), then all directional derivatives of f exist at (0, 0).b)If all directional derivatives of f exist at (0, 0), then f is differentiable at (0, 0).c)If all directional derivatives of f exist at (0, 0), then f is continuous at (0, 0).d)If the partial derivativesexist and are continuous in a disc centered at (0,0) then f is differentiable at (0, 0).Correct answer is option 'A,D'. Can you explain this answer?
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Let be a function. Then which of the following statements is/are TRUE ?a)If f is differentiable at (0, 0), then all directional derivatives of f exist at (0, 0).b)If all directional derivatives of f exist at (0, 0), then f is differentiable at (0, 0).c)If all directional derivatives of f exist at (0, 0), then f is continuous at (0, 0).d)If the partial derivativesexist and are continuous in a disc centered at (0,0) then f is differentiable at (0, 0).Correct answer is option 'A,D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let be a function. Then which of the following statements is/are TRUE ?a)If f is differentiable at (0, 0), then all directional derivatives of f exist at (0, 0).b)If all directional derivatives of f exist at (0, 0), then f is differentiable at (0, 0).c)If all directional derivatives of f exist at (0, 0), then f is continuous at (0, 0).d)If the partial derivativesexist and are continuous in a disc centered at (0,0) then f is differentiable at (0, 0).Correct answer is option 'A,D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let be a function. Then which of the following statements is/are TRUE ?a)If f is differentiable at (0, 0), then all directional derivatives of f exist at (0, 0).b)If all directional derivatives of f exist at (0, 0), then f is differentiable at (0, 0).c)If all directional derivatives of f exist at (0, 0), then f is continuous at (0, 0).d)If the partial derivativesexist and are continuous in a disc centered at (0,0) then f is differentiable at (0, 0).Correct answer is option 'A,D'. Can you explain this answer?.
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