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Consider f : ℝ→ℝ defined by
Then which of the following statements is correct?
  • a)
    Both the partial derivatives of f at (0,0) exist.
  • b)
    The directional derivative  f(0.0) of f at (0,0) exist for every unit vector 
  • c)
    f is continuous at (0,0).
  • d)
    f is differentiable at (0,0).
Correct answer is option 'B'. Can you explain this answer?
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Consider f :2→defined byThen which of the following statements is...
Let y = mx2, then
depends on the value of m. Hence, ,  f(x,y) do not exist.
Hence, f isnotcontinuous at (0,0). Therefore, f is not differentiable at (0,0).
For v2= 0, means that it is partial derivative with respect tox, which exists at (0,0).
Hence, directional derivative exists for everyunit vector .
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Consider f :2→defined byThen which of the following statements is correct?a)Both the partial derivatives of f at (0,0) exist.b)The directional derivativef(0.0) of f at (0,0) exist for every unit vectorc)f is continuous at (0,0).d)f is differentiable at (0,0).Correct answer is option 'B'. Can you explain this answer?
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Consider f :2→defined byThen which of the following statements is correct?a)Both the partial derivatives of f at (0,0) exist.b)The directional derivativef(0.0) of f at (0,0) exist for every unit vectorc)f is continuous at (0,0).d)f is differentiable at (0,0).Correct answer is option 'B'. 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 Consider f :2→defined byThen which of the following statements is correct?a)Both the partial derivatives of f at (0,0) exist.b)The directional derivativef(0.0) of f at (0,0) exist for every unit vectorc)f is continuous at (0,0).d)f is differentiable at (0,0).Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider f :2→defined byThen which of the following statements is correct?a)Both the partial derivatives of f at (0,0) exist.b)The directional derivativef(0.0) of f at (0,0) exist for every unit vectorc)f is continuous at (0,0).d)f is differentiable at (0,0).Correct answer is option 'B'. Can you explain this answer?.
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