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Consider the function f = |5-4x| and refer to the following options.
  • a)
    Is continuous and differentiable for all real values of x
  • b)
    Is continuous for all real values of x and differentiable for all real values of x except x=4/5
  • c)
    Is continuous for all real values of x and differentiable for all real values of x except x=5/4
  • d)
    Is continuous for all real values of x except x=4 and differentiable for all real values of x
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Consider the functionf =|5-4x|and refer to the following options.a)Is ...

Since the function is polynomial in both the cases, it is continuous.
Left Hand Derivative=-4
Right hand Derivative= +4
Since LHD≠RHD, the function is not differentiable at x=5/4.
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Consider the functionf =|5-4x|and refer to the following options.a)Is continuous and differentiable for all real values of xb)Is continuous for all real values of x and differentiable for all real values of x except x=4/5c)Is continuous for all real values of x and differentiable for all real values of x except x=5/4d)Is continuous for all real values of x except x=4 and differentiable for all real values of xCorrect answer is option 'C'. Can you explain this answer?
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Consider the functionf =|5-4x|and refer to the following options.a)Is continuous and differentiable for all real values of xb)Is continuous for all real values of x and differentiable for all real values of x except x=4/5c)Is continuous for all real values of x and differentiable for all real values of x except x=5/4d)Is continuous for all real values of x except x=4 and differentiable for all real values of xCorrect answer is option 'C'. 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 Consider the functionf =|5-4x|and refer to the following options.a)Is continuous and differentiable for all real values of xb)Is continuous for all real values of x and differentiable for all real values of x except x=4/5c)Is continuous for all real values of x and differentiable for all real values of x except x=5/4d)Is continuous for all real values of x except x=4 and differentiable for all real values of xCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the functionf =|5-4x|and refer to the following options.a)Is continuous and differentiable for all real values of xb)Is continuous for all real values of x and differentiable for all real values of x except x=4/5c)Is continuous for all real values of x and differentiable for all real values of x except x=5/4d)Is continuous for all real values of x except x=4 and differentiable for all real values of xCorrect answer is option 'C'. Can you explain this answer?.
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