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 Af(x) is differentiable at x=3π2. Cf(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.