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Question

# Let f(x)=[17+4sinx], x∈[π,2π]. Then which of the following statement is/are correct ? ( [.] denotes the greatest integer function )

A
f(x) is differentiable at x=3π2.
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B
f(x) is non-differentiable exactly at 8 points.
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C
f(x) is non-differentiable exactly at 6 points.
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D
f(x) is non-differentiable exactly at 7 points
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Solution

## The correct options are A f(x) is differentiable at x=3π2. C f(x) is non-differentiable exactly at 6 points.f(x)=17+[4sinx], Now checking continuity and differentiability of [4sinx] by graph, From graph it is clear that f(x) is non-differentiable at 6 points. f(x) is differentiable at x=3π2

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