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Let f(x) = | sin πx |, then
  • a)
    f is continuous nowhere
  • b)
    f is continuous everywhere and differentiable nowhere.
  • c)
    f is continuous everywhere and differentiable every where except at integral values of x.
  • d)
    f is differentiable everywhere.
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Let f(x) = | sin πx|,thena)f is continuous nowhereb)f is continuous...
The graph of the function f(x) = | sinπx | is y =f(x)

clearly, the graph have sharp edges at the points 0, ±1, ± 2, ±3, .. therefore function is continuous everywhere but not differentiable everywhere except at integral values of x.
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Most Upvoted Answer
Let f(x) = | sin πx|,thena)f is continuous nowhereb)f is continuous...
The graph of the function f(x) = | sinπx | is y =f(x)

clearly, the graph have sharp edges at the points 0, ±1, ± 2, ±3, .. therefore function is continuous everywhere but not differentiable everywhere except at integral values of x.
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Community Answer
Let f(x) = | sin πx|,thena)f is continuous nowhereb)f is continuous...
The graph of the function f(x) = | sinπx | is y =f(x)

clearly, the graph have sharp edges at the points 0, ±1, ± 2, ±3, .. therefore function is continuous everywhere but not differentiable everywhere except at integral values of x.
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Let f(x) = | sin πx|,thena)f is continuous nowhereb)f is continuous everywhere and differentiable nowhere.c)f is continuous everywhere and differentiable every where except at integral values of x.d)f is differentiable everywhere.Correct answer is option 'C'. Can you explain this answer?
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